1. Show that if pla + a + a? + a+1 and a -1 mod 5 then P=1 mod 5. Hint: a -1= (a - 1)(a* +a + a? + a+1). What is the period of powers of a when seen modulo p? 2. Show that there are infinite many primes p such that pl mod 5. Hint: if p, P , Pa are the first n primes consider A + A+ A? + A'+1 where 10p, PPs.. Pa-1. A =

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1. Show that if pla* + a + a? +a+1 and a -1 mod 5 then
p=1 mod 5.
Hint: a -1= (a - 1)(a' +a + a? +a+1). What is the period of powers of a when seen modulo p?
2. Show that there are infinite many primes p such that
p=1 mod 5.
Hint: if pi, P2,. Pn are the first n primes consider A+ A+ A? + A' +1 where
10p, PaPs... Pa -1.
A=
Transcribed Image Text:1. Show that if pla* + a + a? +a+1 and a -1 mod 5 then p=1 mod 5. Hint: a -1= (a - 1)(a' +a + a? +a+1). What is the period of powers of a when seen modulo p? 2. Show that there are infinite many primes p such that p=1 mod 5. Hint: if pi, P2,. Pn are the first n primes consider A+ A+ A? + A' +1 where 10p, PaPs... Pa -1. A=
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