2^n-1 Mod n Rechenen?

2^n mod n – OeisWiki – On-Line Encyclopedia of Integer …

2 n ≡ 1 (mod n) 2 n ≡ 1 (mod n) has the only solution n = 1. Proof. Assume that there exists a solution n > 1. Consider its smallest prime divisor p. Then 2 …

elementary number theory – Prove that $a^{2^n}=1 \mod …

I would like to prove that $$a^{2^n}\equiv 1 \pmod {2^{n+2}}$$ I tried induction but could not get it. Thank you very much!

Why does 2^n != 1 (mod n) is true for every n > 1 …

2009-11-07 · Why does: 2^n != 1 (mod n) for every n > 1? Is there any „simple“ proof of this fact? Chris

On the Congruence 2 2 = 1 (mod n)

 · PDF file

mathematics of computation volume 43, number 167 july 1984. pages 271-272 On the Congruence 2″ 2 = 1 (mod n) By A. Rotkiewicz Abstract. There exist infinitely many positive integers n such that 2″~2 = 1 (mod n).

nt.number theory – b^(n-1)=-1 mod n – MathOverflow

By Fermat’s little theorem we know that $$b^{p-1}=1 \mod p$$ if p is prime and $\gcd(b,p)=1$. On the other hand, I was wondering whether $$b^{n-1}=-1 \m…

$1^n +2^n + \\cdots +(p-1)^n \\mod p – Stack Exchange

Calculate for every positive integer $n$ and for every prime $p$ the expression $$1^n +2^n + \cdots +(p-1)^n \mod p$$ I need your help for this. I …

math – Calculating and printing (2^N-1) mod (10^9 + 7) …

I have a certain problem where I’m given a list of T numbers (T is the first line of the input) called N, and I must print out ((2^N)-1)%(10^9+7) for each of the numbers.

Primitive root modulo n – Wikipedia

In modular arithmetic, a branch of number theory, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n.That is, for every integer a coprime to n, there is an integer k such that g k ≡ a (mod n).

Elementary example ·

math – Computing (a*b) mod c quickly for c=2^N +-1 – …

But I’ve been told that there are special tricks for efficiently computing a*b mod C when C is of the form (2^N)-1 or (2^N)+1, …

Modulo operation – Wikipedia

In computing, the modulo operation finds the remainder after division of one number by another (sometimes called modulus).. Given two positive numbers, a (the dividend) and n (the divisor), a modulo n (abbreviated as a mod n) is the remainder of the Euclidean division of a by n.

Remainder … ·