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Number Theory
Level
3
the square of any odd number when divided by a number A gives a constant remainder B every time. So find the sum of maximum possible number A and the constant remainder B. i.e. find( A+B)
The answer is 9.
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1 solution
An odd number 'x' can be written in the form of x=2n-1.
Now x^2 = 4n^2-4n+1 = 4n(n-1)+1
4n(n-1) will always be divisible by an 8 because either n or n-1 will be even. The constant remainder is 1.
So the answer is 8+1=9