garnirativ8

garnirativ8

Answered

2022-10-07

Every odd prime can be expressed as the difference of two squares in one and only one way.
​(a) Find this one way for the prime number 37
​(b) Find this one way for the prime number 41

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Answer & Explanation

goffaerothMotw1

goffaerothMotw1

Expert

2022-10-08Added 10 answers

Step 1
a) x 2 y 2 = 37
( x + y ) ( x y ) = 37
let x + y = 37
x y = 1
Add both 2 x = 38
x = 38 / 2
x = 19
hence y = 37 19 = 18
Thus 37 = 19 2 18 2
Step 2
b) x 2 y 2 = 41
( x + y ) ( x y ) = 41
let x + y = 41
x y = 1
Add both 2 x = 42
x = 42 / 2
x = 21
hence y = 41 21 = 20
Thus 41 = 21 2 20 2

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