number theory b Find x such that x2 3 mod 1297 You can use a

number theory

b) Find x such that x2 3 mod 1297. You can use a calculator, You could just try every x from 1 to 648 until you found a solution.)

2x = 3 mod 1297

gcd(2,1297) = 1 therefor it has unique solution

Therefore, it is equivalent to x = 3k mod 1297

where 2k = 1 mod 1297

Then k = 649

now x = 3*649 mod 1297

which is same as x = 650 mod 1297

now this has many solutions but not in the range of 1 to 648.