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
Number Theory

12/04/16

which of the follwing is between 1/2 and 1/3?

2/5 1/4 2/7 or 3/11  
Number Theory Set Theory Abstract Groups

11/29/16

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  
Number Theory

09/30/16

Pyramid problem

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
Number Theory

07/28/16

last two digit

What would be last two digit of 2563 x 6325 .

05/11/16

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

04/22/16

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
Number Theory Division Congruences

03/13/16

Finding remainder

What is the remainder when 47338 is divided by 5?
Number Theory Algebra

03/13/16

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)
Number Theory Discrete Math Ana

03/10/16

compute 4^123 mod 7

  Hello  I want help with compute 4^123 mod 7   thanks
Number Theory

02/06/16

What is that product of the next two consecutive even integers?

Let x be an even integer.  
Number Theory

09/27/15

Find the number of solutions in integers(x,y) of the equation x^2 y^3=6^12

help..pls.. number theory..
Number Theory

08/22/15

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.
Number Theory

08/21/15

show that the following is an integer

(√2)∧(√2) ∧(√2) ∧(√2) ∧.......
Number Theory

12/07/12

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

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