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2.6 Consider all the possible sets of two square roots s, t of 1 (mod 35)...

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Advance Math

2.6 Consider all the possible sets of two square roots s, t of 1(mod 35) where s ≢ t (mod 35) (there are six of them, sinceaddition is commutative (mod 35). For all possible combinations,compute gcd(s + t, 35). Which combinations give you a single primefactor of 35?

2.7 Using CRT notation, show what is going on for all thecombinations you considered in #2.6. Explain why gcd(s + t, 35)sometimes gave you a factor, and it sometimes did not.

2.8 Explain how you can make a digital signature that ismathematically equivalent to factoring using the results youconsidered in this assignment.

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