For which of the numbers, from n = 2 to 8, is 2n – 1 a prime? - Sarthaks eConnect | Largest Online Education Community
![number theory - Show that $2^{2^n} = (\prod {p_i^{a_i}}\equiv 2^{n+1 }\alpha_ix_i+1) \mod 2^{2n+2}\implies 2^{n+1} (x_1 \alpha_1 + \dots + x_k\alpha_k ) $ - Mathematics Stack Exchange number theory - Show that $2^{2^n} = (\prod {p_i^{a_i}}\equiv 2^{n+1 }\alpha_ix_i+1) \mod 2^{2n+2}\implies 2^{n+1} (x_1 \alpha_1 + \dots + x_k\alpha_k ) $ - Mathematics Stack Exchange](https://i.stack.imgur.com/IBiS1.png)
number theory - Show that $2^{2^n} = (\prod {p_i^{a_i}}\equiv 2^{n+1 }\alpha_ix_i+1) \mod 2^{2n+2}\implies 2^{n+1} (x_1 \alpha_1 + \dots + x_k\alpha_k ) $ - Mathematics Stack Exchange
![SOLVED: If n is a nonnegative integer, must 2^2^n + 1 be prime? Prove or give a counterexample. I know that there is a working number if you plug in 5, but SOLVED: If n is a nonnegative integer, must 2^2^n + 1 be prime? Prove or give a counterexample. I know that there is a working number if you plug in 5, but](https://cdn.numerade.com/ask_previews/7d7032b9-a529-40dc-8466-2ccedf07f89b_large.jpg)
SOLVED: If n is a nonnegative integer, must 2^2^n + 1 be prime? Prove or give a counterexample. I know that there is a working number if you plug in 5, but
![If 2n+1 is a prime number, show that 1^2, 2^2, 3^2,,,,,n^2 when divided by 2n+1 leave different remainders. If 2n+1 is a prime number, show that 1^2, 2^2, 3^2,,,,,n^2 when divided by 2n+1 leave different remainders.](https://haygot.s3.amazonaws.com/questions/1575330_1745475_ans_52f2f9a51794480c842cc778b1592190.jpg)
If 2n+1 is a prime number, show that 1^2, 2^2, 3^2,,,,,n^2 when divided by 2n+1 leave different remainders.
If [math]P[/math] is a prime number and [math]P_1[/math] is the previous prime number, I've found that [math]P_1-\frac{P_1^2}{P}[/math] tends to an even integer as [math]P[/math] increases. Can this be proved? - Quora
![number theory - Are there infinitely many primes of the form $k\cdot 2^n +1$? - Mathematics Stack Exchange number theory - Are there infinitely many primes of the form $k\cdot 2^n +1$? - Mathematics Stack Exchange](https://i.stack.imgur.com/iScA0.jpg)