2^100 - 2^96 = 2^96*2^4 - 2^96

= 2^96 ( 2^4 - 1 )

= 2^96 ( 16 - 1 )

= 2^96 ( 15 )

Therefore, 2^96 has prime number 2 repeated 96 times. 15 has prime numbers 3 and 5. Since the question asks for the greatest prime number that divides them, 5 it is.

The other question is better explained with a diagram but as I said in a previous post, I suck at drawing those. Maybe I'll try later but that question is easier than the second one. It's about applying pythagore and knowing the hypothenuse.

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Best Regards,

Paul