67 Answered Questions for the topic Number Theory

12/20/16

#### 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

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...
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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...
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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...
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Number Theory Algebra

03/13/16

#### What is the remainder?

What is the remainder when 4175 is divided by 3?

03/13/16

#### 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...
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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

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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