21.) If A And B Are Positive Integers Such That A/B=113.3125,then What Is The Smallest Value Of B Such That (A*A-4)is Divisible By B?


3 Answers

Oddman Profile
Oddman answered
The problem only has one solution, B = 32, A = 3626.

I have not been schooled in Diophantine equations, as you probably have. My approach is this.
I substituted A = 1813B/16 into the expression (A*A-4)/B and set the result equal to N. Solving for B gives
  B = 32(4N + √(1813^2 + 16N^2))/1813^2 = 32m
I solved for N and found
  N = (3286969*m^2 - 1)/(8*m)
The only value of m that can satisfy this is m=1.
Anonymous Profile
Anonymous answered
10.) If A and B are positive integers such that
A/B=113.3125,then what is the smallest value of B such that (A*A-4)is divisible
by B?

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