# Hard Math

I remember some math questions from the math Olympiads, so can you do better than I can? Good luck!

1) a-squared +b-squared=2018-2a, what is a and b?

2) What is the last non-0 digit of 50!

3a) a and b are positive integers, where a= the sum of all the digits of a and b, and b= the product of all the digits of a and b. Find all pairs that satisfy this equation, under 100.

3b) FInd all pairs under 1000, and one of the numbers has to be over 99.

Really, I only got an answer for 2 (probably wrong), and nothing for the rest. Please tell me what you got, and please note, I might have remembered this wrong. But, it should still be right. How did you go? :)

Note by Caleb Kum
1 year, 10 months ago

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Q1) The answer is that there are no possible INTEGRAL a and b satisfying the equation..................otherwise there are infinitely many pairs of a and b..........

- 1 year, 10 months ago

What I found that it may seem like that, but when I did it, it would always be short. So, (Idk if this is right) there should be only one answer.

- 1 year, 10 months ago

I rechecked my calculations and found no error..........Check again..........There are no Integral a and b satisfying the condition...........If you have found a solution, then tell me the answer....... :)

- 1 year, 10 months ago

Ok, I'll take your word for it. Hey, anyone, can YOU find an answer? (I can't be stuffed to do so).

- 1 year, 10 months ago