# Dwayne E. Pouiller

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# 31 Questions

 7 For which primes p is $p^2 + 2$ also prime? 5 Colored Picture for Equivalence Classes, Relations, Partitions, .. 5 Do Question's Given GCD Statements Imply these New GCD Statements? 5 Proof - There're infinitely many primes of the form 3k + 2 — origin of $3q_1..q_n + 2$ 5 Intuition — c|a and c|b if and only if $c| \gcd(a,b)$.

# 470 Reputation

 +10 Ground plan of Forward direction - Let $p$ be an odd prime. Prove $x^{2} \equiv -1 \; (mod \, p)$ has a solution $\iff p\equiv 1 \; (mod 4)$ +5 Ground plan of Backward direction (<=) - Let $p$ be an odd prime. Prove $x^{2} \equiv -1 \; (mod \, p)$ has a solution $\iff p\equiv 1 \; (mod 4)$ +5 Fermat's Little Theorem fails for composite instead of prime numbers. -2 Colored Picture for Equivalence Classes, Relations, Partitions, ..

 5 GCD is MIN of Exponents of Prime Factors, LCM is MAX of Exponents of Prime Factors. 5 If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$ 5 If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$ 3 Can't understand a proof: Let $a,b,c$ be integers. If $a$ and $b$ divide $c$, then $lcm(a,b)$ also divides $c$ 3 show that $\gcd(a_1, \dots, a_n) = \gcd(a_1, \dots, a_{n-2},\gcd(a_{n-1},a_n))$

# 20 Tags

 26 elementary-number-theory × 35 0 proof-verification × 10 2 proof-strategy × 16 0 proof-explanation × 8 2 divisibility × 3 0 advice × 4 1 number-theory 0 learning × 2 0 intuition × 11 0 summation × 2

# 3 Accounts

 Mathematics 470 rep 421 French Language 101 rep 1 Area 51 101 rep 2