Asked by whatismath
Prove that 29|2⁹⁰ + 5⁹⁰.
I am not sure how to go about proving this divisiblity problem. Can anyone help me on how to go about the process to solve it? Thanks so much.
I am not sure how to go about proving this divisiblity problem. Can anyone help me on how to go about the process to solve it? Thanks so much.
Answers
Answered by
oobleck
since we're dealing with sum of cubes,
2^90 + 5^90 = (2^30 + 5^30)(2^60-10^30+5^60)
2^30 + 5^30 = (2^10 + 5^10)(2^20-10^10+5^20)
2^10 + 5^10 = 29*336781
2^90 + 5^90 = (2^30 + 5^30)(2^60-10^30+5^60)
2^30 + 5^30 = (2^10 + 5^10)(2^20-10^10+5^20)
2^10 + 5^10 = 29*336781
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