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[SOLVED] Find Integer Solutions for (A+3B)(5B+7C)(9C+11A)=1357911

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anemone

MHB POTW Director
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Feb 14, 2012
3,601
Find all integer solutions (if any) for the equation $(A+3B)(5B+7C)(9C+11A)=1357911$.
 

HallsofIvy

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MHB Math Helper
Jan 29, 2012
1,151
I would start by finding the prime factors of 1375911 (there are five) then forming all groups of 3 factors.
 
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anemone

MHB POTW Director
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Feb 14, 2012
3,601
Hi HallsofIvy !

Thanks for your reply. But since this is a challenge question, I hope you know our expectation here is to receive a full solution, no more, no less. (Happy)
 

kaliprasad

Well-known member
Mar 31, 2013
1,283
No solution because

RHS is odd so all factors are odd so each term in the LHS is odd. there are 3 terms on the LHS and so their sum has to be odd.

but sum is 12A + 8B + 16C which is even so impossible