71 Answered Questions for the topic Number Theory

Number Theory Math Division Problem

07/05/19

How do I solve this problem regarding divisibility from my Math Challenge class?            
What remainder does the number (-50) leave after division by 7? The answer is 6. Why?
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Number Theory Algebra 2

05/05/19

Show that if x,y,z are integers such that x^3 + 5y^3 = 25z^3, then x = y = z = 0.
I tried using mod 5 to get that x is divisible by 5. I don't know much about infinite descent, so I do not think that is the way to go.The hint says "If I give you a non-trivial solution, can you... more
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04/29/19

a,b,c are positive real numbers with abc=1 then prove that (a / a+b⁴+c⁴) + (b / a⁴+b+c⁴) + (c / a⁴+b⁴+c)＜=1
a,b,c are positive real numbersabc=1prove that (a / a+b⁴+c⁴) + (b / a⁴+b+c⁴) + (c / a⁴+b⁴+c)＜=1
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Number Theory

03/24/19

What is the multiplicative inverse of 3 module 46?
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03/19/19

Numbers that are the sum of the squares of their prime factors?
A number which is equal to the sum of the squares of its prime factors with multiplicity: - $16=2^2+2^2+2^2+2^2$ - $27=3^2+3^2+3^2$ Are these the only two such numbers to exist? There has to be... more
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03/19/19

Can it be proven/disproven that there are highly composite numbers that prime-factorize into larger primes such as $9999991$?
Of course, following the rules found by Ramanujan, such a highly composite number would need to factorize into all primes ascending up to 9999991 (with descending powers as the primes progress) so... more
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03/18/19

When is $4n^4+1$ prime?
Find all natural numbers $n$ such that $4n^4+1$ is prime. $4n^4+1$ is obviously prime when $n=1$. But can we prove that no other $n$ works?
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03/15/19

How many primes do I need to check to confirm that an integer $L$, is prime?
I recently saw the 1998 horror movie "Cube", in which a character claims it is humanly impossible to determine, by hand without a computer, if large (in the movie 3-digit) integers are prime... more
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Number Theory Algebra 1 Gre Gre Exam

03/14/19

How many 2-digit positive integers are there?
How many 2-digit positive integers are there such that the product of their two digits is 24? The answer given is four. I'm not certain if I understand this question correctly and need some... more
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03/12/19

Find a prime factor of $7999973$ without a calculator?
How would you go about finding prime factors of a number like $7999973$? I have trivial knowledge about divisor-searching algorithms.
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Number Theory Prealgebra

01/30/19

If a piece of wood 8 3/4 ft long is to be cut into four equal pieces , find the lengt
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Number Theory Math Mathematics

01/18/19

What are the last digits of 3^3^3^3
If Xn=3^3^3.(n times)..^3 with n bigger than 10, show that their 10 last digits are the same. I think we should use Euler Fermat's theorem, and calculate with modulo(10^10) and somehow prove it by... more
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Number Theory

10/26/18

Find the value of an integer a such that a^2 +6a +1 is a perfect square.

I was able to solve this but it required me using hit and trial at one step. I was wondering if i could find a more solid method to solve it.p.s. this is the first time im asking a question here so... more
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Number Theory Logic Numbers Arithmetic

08/08/18

Eric and Marina each wrote two or three poems everyday. Over a period of time, Eric wrote 43 poems while Marina wrote 61.
 How many days were in this period of time?  18,19,20,21, or 22 days   Thanks so much
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Number Theory

03/30/18

what is the prime factorization for 27
 i dont know
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Number Theory Equations

12/23/17

The value of a three digit number increases by 108 when the first digit is placed at the last and the value of the number increases by 189 when ...
Can you solve the problem below: The value of a three digit number increases by 108 when the first digit is placed atthe last and the value of the number increases by 189 when the last number... more
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Number Theory

11/06/17

Why is 2 a controversial number?
I have heard people say 2 is not a prime number and some go as far to say that 2 is not a number all together. What is the meaning behind this? Have I been lied to my entire life?
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10/08/17

Explain why gcd(a, b) = 1.
If 1 = sa + tb, where a, b, st ∈ Z, explain why gcd(a, b) = 1.    
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10/08/17

Show [n(n^2−1)]/3 is an integer
Use the division algorithm to show [n(n^2−1)]/3 is an integer, for all n ∈ Z.
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Number Theory Progressions

08/25/17

Integers 1,2,3.....n are written on a board. Two numbers m,k are removed and average of the remaining numbers is 17. What is maximum value of m+n??
n>2 and 1<m<n and 1<k<n
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Number Theory

08/21/17

1+2-3=0; 1+2+3+...+12+13+14-15-16-...-19-20=0; why does this only occur for numbers (3,20,119,696...) which are leg-leg twin pythagorean triples?
The pivot point (+13+14-15) (+83+84-85) tends to the 1/√2 of the sum. So 14/20, then 84/119, then 492/696 is tending toward 1/√2. 
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Number Theory

08/20/17

find the number of positive integer n, such that √n + √n+1 < 11
Based on number theory
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Number Theory

08/20/17

Find the number of positive integer n, such that √n + √n+1 < 11
This question is prmo 2017. Based on number theory.
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Number Theory

08/20/17

find the number of positive integer n, such that √n + √n+1 < 11
This question is prmo 2017. Based on number theory
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Number Theory Real Numbers

05/07/17

Find a ÷ b
a=(1÷√1)+(1+√3)+(1÷√5).....  b=(1÷√2)+(1÷√4)++(1÷√6).....
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