Post cool algebra problems to solve. List difficulty. Use the link provided to compute them if you have to.

Unrelated but according to WolframAlpha x/0 equals infinity.

IF YOU DON'T START POSTING IN THIS THREAD SOON YOU WILL DIE!!

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Prove that every even integer greater than 2 can be expressed as the sum of two primes.

find a prime number larger than 2^{(10122)}.

Prove Lagrange's Theorem: If H is a subgroup of the finite group G, then the order of H divides (ie. is a divisor of) the order of G.

Euler's Theorem, if gcd(a,n)=1 then a^phi(n) is congruent to 1 (mod n), is corollary to that. Prove that too.

Prove another corollary: Any group of prime order is cyclic.

PS. phi(n) is the number of positive integers less than or equal to n which are relatively prime to n.

PS. Lagrange's Theorem is my favorite theorem because it has so many nice corollaries.

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and finally step 2:

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