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Superincreasing Sequence and Prove that Expression is Prime

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1) Let S= {b ,b ,...........b } satisfies b j+1 >2b j for all j =1,2,3,.......n-1. Prove that S is a superincreasing sequence. ≡

2) Prove that n E N with n ≥ 3 is prime if and only if there exists an integer m such that m^(n-1) ≡ 1 (mod n)^((n-1)/q) but m is not ≡ ( mod n) for any prime q| (n-1)

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A Superincreasing Sequence and a prime expression are investigated. The superincreasing sequences are examined.

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1. Proof:
We know that a sequence is superincreasing if . In this problem, we are given with , . Then we have
,
More generally, for any ...

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