Using difference of squares find all positive integer solutions to the given equ

Question

Using difference of squares find all positive integer solutions to the given equation. Give a clear and concise example, no guessing and checking m^2-n^2=81. This is for discrete math Using difference of squares find all positive integer solutions to the given equation. Give a clear and concise example, no guessing and checking m^2-n^2=81. This is for discrete math Using difference of squares find all positive integer solutions to the given equation. Give a clear and concise example, no guessing and checking m^2-n^2=81. This is for discrete math

Explanation / Answer

solution--:

case-1
(m - n) (m + n) = 1 * 81 ( odd * odd case )

m-n=1, m+n = 81

2m=82 m = 41

41+n=81

n=81-41=40

m= 41, n= 40

also case 2

(m+n)(m-n) = 9 * 9 odd odd case

m+n = 9, m-n= 9

2m =18

m= 9

n=0

m=9, n=0

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