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Question 30965: The sum of two consecutive odd integers is at most 123. Find the pair with the greatest sum.
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! The sum of any two odd integers is even. That's because odd = even + 1
odd[1] = even[1] + 1
odd[2] = even[2] + 1
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odd[1] + odd[2] = even[1] + even[2] + 2
The right side is definitely even
so the sum of the two consecutive odd integers can't be 123. I'll try 122
An odd integer can be expressed as 2n+1. Whatever n is, 2n+1 is guaranteed to be odd
The next odd integer is 2n + 3
(2n+1) + (2n+3) = 122
4n + 4 = 122
2n + 2 = 61
2n = 59
2n + 1 = 60
this needs to be odd for n to be an integer, so I'll call it 59
The next odd integer is 61
59 + 61 = 120
I'll see if the next consectutive pair is greater than 123
61 + 63 = 124
It is greater, so the answer is 59 and 61
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