- #1

- 342

- 0

a) 2

^{293}[itex]\equiv[/itex] x (mod 15)

b) 243

^{101}[itex]\equiv[/itex] x(mod 8)

c) 5

^{2001}+ (27)! [itex]\equiv[/itex] x (mod 8)

a) I was able to equate 2[itex]\equiv[/itex]-13(mod15) ==> 2

^{2}[itex]\equiv[/itex]4(mod15)

my idea here was to get 2

^{9}and then multiply by a power of 100 which would give me 900 and then work out the other 23 from there, but I've already hit a road block....I'm going to end up with a huge number just from the product of the moduluses......maybe that's what is suppose to happen, but I'm under the assumption that I'm suppose to figure these out without a calculator.

b) I was able to work it down to a congruence of 243 [itex]\equiv[/itex] 3(mod 8) but if I raise that to the 101 on both sides.....again I'm out of luck in terms of the 3.

help please.......