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Factor hints II (Posted on 2019-04-20)

399337 = 616² + 141²
399337 = 464² + 429²

Based on the above results find the two prime factors of 399337.

No Solution Yet Submitted by Danish Ahmed Khan

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Longhand

Comment 1 of 1

Using a method of Euler:

Let a=616, b=141, c=464, d=429

Then

a-c=152 2^3*19

a+c=1080 2^3*3^3*5

d-b=288 2^5*3^2

d+b=570 2*3*5*19

GCD(152,288)=8

GCD(1080,570)=30

GCD(152,570)=38

GCD(1080,288)=72

399337=((8/2)^2+(30/2)^2)*((38/2)^2+(72/2)^2) = 241*1657

Posted by broll on 2019-04-22 10:56:40

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