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squaremeplz
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Homework Statement
Find x for
ax = 1 (mod m)
a) a = 15 , m = 31
b) a = 6, m = 93
c) a = 15, m = 20
if possible.
(The equal sign above is equivalence in modular arithmetic)
Homework Equations
The Attempt at a Solution
a) gcd(31,5) = gcd( 31 - 2*15, 15) = 1
thus (1)(31) + (-2)(15) = 1
and (-2) * 15 = 1 (mod 31)
i don't understand how I can find x since multiplying by -2 yields a number smaller than the modulus
b) gcd(93,6) = 3
no solution because gcd =/= 1
c) gcd(20,15) = 5
no solution
Could somebody please help me out with these problems. It's my first time doing modular arithmetic and the book has only two examples.
Thank you!
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