Find all integer solutions (if any) for the equation $(A+3B)(5B+7C)(9C+11A)=1357911$.
May 16, 2020 #1 anemone Gold Member MHB POTW Director 3,884 11,585 Find all integer solutions (if any) for the equation $(A+3B)(5B+7C)(9C+11A)=1357911$.
May 16, 2020 #2 HallsofIvy Science Advisor Homework Helper 43,010 973 I would start by finding the prime factors of 1375911 (there are five) then forming all groups of 3 factors.
I would start by finding the prime factors of 1375911 (there are five) then forming all groups of 3 factors.
May 16, 2020 #3 anemone Gold Member MHB POTW Director 3,884 11,585 Hi HallsofIvy! Spoiler 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)
Hi HallsofIvy! Spoiler 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)
May 16, 2020 #4 kaliprasad Gold Member MHB 1,337 0 Spoiler: my Solution 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
Spoiler: my Solution 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