Realize that I am not the OP. And that I am not asking the Dr. to do this, unless he wishes to.
Quote:
Originally Posted by Dr. Silverman
Let a_i = N mod p_i for p_i = 2,3,5,7,11.....
up to some selected bound.
If N is a kth power, then it will be a kth power mod each of the primes.
If it fails any prime, then it is not a k'th power. Or one could check
if it is a kth power mod 2*3*5*7*11.... etc. (i.e. check all primes at
once)
If it is a kth power mod each prime, then we suspect that it actually
is a kth power.

Could someone show an example of this, with a real pair of numbers (say, 62748517 =13^7 and 62748571 [a random similar numbr]). I kinda get lost in the highlighted section. I think that I can grasp most of the rest and looked briefly at Newton's method (successive approx.) and get that.
Thanks