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# maths question again (try this) watch

1. sum of the digits of

444,444,444,444,445^2 - 555,555,555,555,555^2

sorry edited by accident
2. -111111111111111111111111111111

MdSalih
3. that;'s not the sum of digits though :-)
4. The number is -11...1(14 digits) x 10^16
So the sum of digits is 14
5. well done

harder question
what three digit number divides (2^32 + 1)?
6. (Original post by mik1w)
well done

harder question
what three digit number divides (2^32 + 1)?
641 divides F_5

(c) Mr Euler
7. (Original post by mik1w)
well done

harder question
what three digit number divides (2^32 + 1)?
The more interesting question is how do we know that F_5 is divisible by 641?

Let a=2^7, b=5, so that a - b^3 = 3, 1+ab-b^4=1+3b=2^4

Therefore,

2^(2^5) + 1 = (2a)^4 + 1 = (1 + ab - b^4)a^4 + 1 = (1+ab)a^4 + 1 - (a^4)(b^4), and this must be divisible by 1+ab=2^4 + 5^4=641
8. (Original post by MdSalih)
-111111111111111111111111111111

MdSalih
Just wondering why imperial is your first choice, not Cambridge?
9. i am wondering as well

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