- #1
trap101
- 342
- 0
find the remainders for
a) 2293[itex]\equiv[/itex] x (mod 15)
b) 243101[itex]\equiv[/itex] x(mod 8)
c) 52001 + (27)! [itex]\equiv[/itex] x (mod 8)
a) I was able to equate 2[itex]\equiv[/itex]-13(mod15) ==> 22[itex]\equiv[/itex]4(mod15)
my idea here was to get 29 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...
a) 2293[itex]\equiv[/itex] x (mod 15)
b) 243101[itex]\equiv[/itex] x(mod 8)
c) 52001 + (27)! [itex]\equiv[/itex] x (mod 8)
a) I was able to equate 2[itex]\equiv[/itex]-13(mod15) ==> 22[itex]\equiv[/itex]4(mod15)
my idea here was to get 29 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...