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[quote="jinino"]I do not get either Bhimsen or Banerjeea_98's approach. Can someone show me the light and explain a bit more in details?

Thanks!

:oops:[/quote]

jinino, 5^40+5^37 can be written as 5^37(5^3+1) which again means 5^37(126). There is only 1 prime factor in 5^37 i.e. 5 and there are 3 prime factors for 126 (2x7x3x3) i.e. 3, 7, 2. Hence ans is 4. Hope this helps.

Thanks for your input. I got it now, but I still have one more question. We know 5^37 has only one prime number, which is 5. What do we do if the question is 6^40+6^37? How do we figure out the prime number for 6^37?

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