Microsoft OFFICE verification key?

You should be wary when you don't use some piece of information given, and so end up proving something stronger than what was asked. In this case it can be easily seen that if we let c = 1 then the statement does not hold, so you *must* incorporate the information c is even somewhere in your proof. Since you didn't, we can immediately see that your proof is not valid.

Going through line by line gcd(c+1, 1) = 1 is true for arbitrary integer c, but does not help prove what you want. Gcd(c+1, c) = 1 is true for arbitrary integer c, but the reason is not "since c does not divide c + 1". Note that gcd(4,6) = 2 even though 4 does not divide 6.

Gcd(c+1, c^2) = 1 is true for arbitrary integer c, but doesn't help prove what you want. Also, "by Euclid's Lemma" is not sufficient justification. You provided no justification going from your second-to-last line to your last line.

You should know that for arbitrary integers x,y,z, we have x | y and x | z implies x | y + z and x | y - z. So, we can prove as follows: Let gcd(c+1, c^2+1) = d So d | (c^2 + 1 - (c + 1)) implies d | (c^2 - c) implies d | ( (c)(c-1) ).

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.