SOLUTION: A number n is 1 plus the sum of the squares of three consecutive odd integers. what is the largest integer factor of all such numbers n?

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Question 251658: A number n is 1 plus the sum of the squares of three consecutive odd integers. what is the largest integer factor of all such numbers n?
Answer by vksarvepalli(154) About Me  (Show Source):
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let the 3 consecutive odd no.s be 2t-1, 2t+1, 2t+3
so n= 1%2B%282t-1%29%5E2%2B%282t%2B1%29%5E2%2B%282t%2B3%29%5E2
expanding the terms and simplifying we get
n=12%28t%5E2%2Bt%2B1%29
so the largest common factor of all such no.s n is 12.
ans: 12