![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
![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)
number theory - Are there infinitely many primes of the form $k\cdot 2^n +1$? - 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
![SOLVED: Prove that there exists a unique prime number of the form n^2 - 1, where n is an integer and n ≥ 2. SOLVED: Prove that there exists a unique prime number of the form n^2 - 1, where n is an integer and n ≥ 2.](https://cdn.numerade.com/ask_previews/4403145e-c91d-4055-a011-aa0ba6d65c7f_large.jpg)
SOLVED: Prove that there exists a unique prime number of the form n^2 - 1, where n is an integer and n ≥ 2.
![number theory - Does $lcm\{1,2,...,n\} = \prod_{p\leq n, p\in\mathbb{P}}p^{\lceil \frac{log(n)}{log(p)}\rceil}$? - Mathematics Stack Exchange number theory - Does $lcm\{1,2,...,n\} = \prod_{p\leq n, p\in\mathbb{P}}p^{\lceil \frac{log(n)}{log(p)}\rceil}$? - Mathematics Stack Exchange](https://i.stack.imgur.com/nnC6x.png)
number theory - Does $lcm\{1,2,...,n\} = \prod_{p\leq n, p\in\mathbb{P}}p^{\lceil \frac{log(n)}{log(p)}\rceil}$? - Mathematics Stack Exchange
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
![T Madas. A prime number or simply a prime, is a number with exactly two factors. These two factors are always the number 1 and the prime number itself. - ppt download T Madas. A prime number or simply a prime, is a number with exactly two factors. These two factors are always the number 1 and the prime number itself. - ppt download](https://images.slideplayer.com/25/7820136/slides/slide_21.jpg)