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Sunday, June 12, 2022

2022/046) Find all n such that 7 | 2^n-1 and show that there is no positive n such that 7 | 2^n + 1 (IMO 1964 problem 1)

because 7 is a prime so as per Fermats Little theoren 

7 | 2^6-1

now as 2^6 leaves remainder 1 after dividing by 7 so it may be taht for some factor a of 6 7 | 2^a-1

we need to check for 1,2,3

so see 2^1-1 = 1 2^2-1 = 3 and 2^3 - 1 = 7 out f these 3 3 satisfies

as so k = 3m for all m satisfies.

Further 2^1+1 = 3 2^2+1 = 5 and 2^3 +1 = 9 out f these 3 none is divsible by 7 so there is no n such that 7 | 2^n+1 

proved 


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