any help on getting started with these would be great. I seem to be having a dead brain day.
- Let p be a prime number.Suppose you take all the non zero integers 0,1,2,...,p-1, multiply them together, and take the answer modulo p.Show that you will always get p-1
- Determine which of 1,2,3,4,5,6,7,8,9,10 (the non zero integers modulo 11) are squares modulo 11. Use this to find the roots of x^5 - 1 modulo 11
- Let f(x) be a polynomial with integer coefficients. Show that if the value of f(x) is divisible by r at r consecutive integers, then f(m) is divisible by are for all integers m.
What've you done so far?