what is the hardest math question you had

like what I said above what is the hardest math question you had

1+1

Let a,b and c positive integers. Prove that is impossible to have all of the three numbers a^2+b+c, a+ b^2+c, a+b+c^2 to be perfect squares.

How do you reconcile relativity with quantum theory?

rajatshenoi that is a pretty easy hardest math question

"How much did this wine cost?". Was asked today, as a matter of fact.

Just off the top of my head.

Let's assume all 3 sums can be perfect numbers, then show that it leads to non-integer solutions (or no solutions).

For any perfect square, the distance to the next larger perfect square is 2*root(n)+1

So for a+b+c^2 we can write a+b = 2*root(c)+1
For a+b^2+c we can write a+c = 2*root(b)+1
For a^2+b+c we can write b+c = 2*root(a)+1

Now we have 3 equations and 3 unknown. From this point we just use algebra to solve, and I assume doing so will result in something impossible like a=a+1 , root of negative number , dividing by zero, etc.

Maybe that doesn't work, but it seems good.

Anyway the hardest problems I've had are applied differential equation problems (basically word problems asking you to use calculus, but differential equations are an annoying form of calculus haha  I'll say it like that).

Oh, and chess.com doesn't let me edit posts, so I can't change some things... but hopefully you know what I mean

@godsofhell1235: I’ll give it a go:

a + c = 2b + 1

a + b = 2c + 1

b + c = 2a + 1

(#2-#3) (#4) a - c = 2c - 2a

a - c = -2(a - c)

1 = -2

Q.E.D.

Prove that for n>2 a^n+b^n=c^n with a, b and c three different positive and hole numbers is impossible. Haven't yet had it as a question but it's short and efficient.

Already proven, but it took a professional mathematician seven years, and that’s only the formal proof. The proof itself is far too long and technical to fit into a forum post, so asking about it on here is pretty pointless.

@GMtheforce: If you don't want to use i, there isn't one.

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BTW ! means 1x2x3x4 to the number it's ! by.

yeah

a computer can do that instantly