## Number Theory Resources

(a-b)^2+(b-c)^2+(c-d)^2+(d-e)^2+(e-a)^2>=K(b-d)^2 a,b,c,d,e,k Is Real Number

I have derived the following theorem: Odd positive integer N=6n−1 is a prime iff neither of two diophantine equations 6x^2+(6x−1)y=n 6x^2+(6x+1)y=n has solution...

Should I use mods like mod 5? Or something else? Can someone please tell me how to solve this problem step by step with the answer?  I appreciate it.

Briefly explain how to generate a random prime number with a particular number of bits using a test such as the Miller-Rabin test.   I know how to conduct the Miller-Rabin Test I'm...

Can you solve the problem below: 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 the last number...

Hello. I have a question please help. What is the use of number theory in science and life? Except for cryptography, is it applicable in genetics or engineering or anything else ?! Please give me...

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?

This is a question of Number theory where we need to find the 2 numbers that sum up to 1904 and their HCF and LCM are 23 and 32340 respectively.