67 Answered Questions for the topic Number Theory
let d=(a,b) then a|bc if and only if a/d is a divisor of c
prove it if it is correct or give counterexample if it is falselet d=(a,b) then a|bc if and only if a/d is a divisor of c
which of the follwing is between 1/2 and 1/3?
2/5 1/4 2/7 or 3/11
principal ideal ring
Suppose thatR=R1⊕R2⊕…….⊕Rnwhere each Ri is a principal ideal ring. Verify that R is also a principal ideal ring. please I want help with that
If you have 140 stone blocks, you can build an Egyptian square pyramid whose base has 7 blocks on each side. At the same time, you can arrange those blocks into 35 perfect 2 × 2 squares. Find a... more
last two digit
What would be last two digit of 2563 x 6325 .
Let p be a odd prime, If ord p (a) = h and h is even, then a^(h/2)= -1 mod p
Determine is, in general, true or false. Recall that auniversal statement is true if it is true for all possible cases while it is false if there is even onecounterexample. Be prepared to prove... more
Number Theory No Calculator
Number theory: What are the last 4 digits of 2^503? (No calculator)
This was an extra credit question on a math test (was not related to what we are learning/have learned) Apparently, it's 0008, because 2^X repeats its last 4 digits every 500 numbers in a... more
What is the remainder when 47338 is divided by 5?
Number Theory Algebra
What is the remainder?
What is the remainder when 4175 is divided by 3?
suppose p denotes a prime congruent to 3 modulo 4; use wilson's theorem to prove that
suppose p denotes a prime congruent to 3 modulo 4; use wilson's theorem to prove that (P-1/2)!2 ≡ 1 (mod p) Hint: Prove that ((p-1)/2)!2 ≡ (p-1)! (mod p) Please explain... more
find a solution of each of the following congruences
a. x2≡ -1 (mod 13)b. x2 ≡-1 (mod 17)
compute 4^123 mod 7
Hello I want help with compute 4^123 mod 7 thanks
What is that product of the next two consecutive even integers?
Let x be an even integer.
Find the number of solutions in integers(x,y) of the equation x^2 y^3=6^12
help..pls.. number theory..
Write any four digit number. Repeat the digits to form a eight digit number(eg.-13571357). Show that two of its prime factors are 73 and 137.
Show that two of its prime factors are 73 and 137.
show that the following is an integer
(√2)∧(√2) ∧(√2) ∧(√2) ∧.......
Let p > 3 be a prime, and suppose that p = 3 (mod 4). If q = 2p+1 is also prime show that (2^p) -1 is never prime.
Need help with this promblem for number theory