CAT 2019 Number System Question (Medium)

Question

How many pairs of positive integers satisfy the equation ?

Accepted Answer

Step 1 We are given n 2 m 2 105 This can be written as n 2 - m 2 105 Factor using difference of squares n - m n m 105 We need to find the number of positive integer solutions . Step 2 Since and are positive integers, so are and . We need all factor pairs of 105. The factor pairs of 105 are - - - - L

CAT 2019

Quantitative

Number System

Medium

How many pairs $(m,n)$ of positive integers satisfy the equation $m^2 + 105 = n^2$ ?

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