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A: We can solve this problem using concept of rational number.

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Q: 5. Verify that the prime number 101 divides 52671234505- 57 using Fermat's theorem.

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Q: he first and second derivati nction

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Q: Denote by fn the nth Fibonacci number. Show that when n is a positive integer, fofi + fif2 + ··+…

A: We will use mathematical induction to prove it.

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Q: 4. A property that, two consecutive positive integers are relatively prime. Consider any two…

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A: a)