Recent content by tommy05

Ok, I found a link explaining quadratic residues: http://mathworld.wolfram.com/QuadraticResidue.html However, in its list of quadratic residues (mod n), it says that the quadratic residues (mod 9) are: 1, 4, 7...so 9 is NOT a residue, and hence this doesn't seem to be able to be applied to...

I don't understand the relevance of the post above...

Matt, would it be too much to ask you to expand your modular arithmetic operation or explain it so someone who isn't too familiar with modular arithmetic can understand it? I'm only in first-year calculus right now, so I haven't been exposed to modular arithmetic and residues...(perhaps I'll...

Well, all of the multiples of 3 can be eliminated (as mentioned above) by noting that any multiple of 3 raised to an even power is a multiple of 9: (3Q)^N = 3^N * Q^N = 9^(N/2) * Q^N, and since N is even, N/2 must be an integer. The digits of any multiple of 9, then, add up to 9...

A little while ago I noticed a pattern in the sums of the digits of perfect squares that seems to suggest that: For a natural number N, the digits of N^2 add up to either 1, 4, 7, or 9. ex: 5^2 = 25, 2+5 = 7 In some cases, the summation must be iterated several times: ex: 7^2 = 49...