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Maths Puzzle
The remainder when 17^37+29^37 is divided by 23 is
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- Remainder is 0
(17)^x + (29)^x is always divisible by 23 where x is an odd number
Eg:- 17^3 + 29^3 divisible by 23
=> (17)^37 + (29)^37 divisible by 23
=> remainder is 0. - 12 years agoHelpfull: Yes(2) No(1)
- If n is odd, a^n + b^n = (a + b)(a^(n - 1) - a^(n - 2)*b + a^(n - 3)*b^2 -... + b^(n - 1)).
Therefore, a^n + b^n is divisible by (a + b) when n is odd
so when 17^37+29^37 is divided by 23, remainder is zero as (17^37+29^37) is divisible by (17+29) or 46 which is divisible by 23. - 12 years agoHelpfull: Yes(2) No(0)
- when we apply a remainder theorem then we will get (-6)^37 + (6)^37 and the power is 37 it is odd so (-6)^37 is negative value and
(6)^37 is positive value, both magnitudes are equal then the remainder is zero... - 12 years agoHelpfull: Yes(1) No(0)
- 0
37(17+29)/23=74
remainder 0
- 12 years agoHelpfull: Yes(0) No(2)
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