Question

If 2^{96}-1 is divisible by two integers between 60 and 70, what are the two numbers?

Steven Zheng Steven Zheng posted 2 months ago


Answer

2^{96}-1

=(2^{48}+1)(2^{48}-1)

= (2^{48}+1)(2^{24}+1)(2^{24}-1)

= (2^{48}+1)(2^{24}+1)(2^{12}+1)(2^{12}-1)

= (2^{48}+1)(2^{24}+1)(2^{12}+1)(2^6+1)(2^6-1)

= (2^{48}+1)(2^{24}+1)(2^{12}+1) × 65×63

Steven Zheng Steven Zheng posted 2 months ago

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