Thread: CRT...stuck

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Originally Posted by yellow4321

x congruent 1mod3 (a)
x congruent 2mod4 (b)
x congruent 3mod7 (c)
x congruent 4mod11 (d)

ok my 2nd method failed to give me a right answer for (d) i got 262?so ive been trying another method.heres what ive done so far but im stuck...

taken (a) and (b) tested for numbers up to 12 as (3.4=12) and 10 works for both so then i take

x congruent 10mod12 and (c)

(12.7=84) so i test for numbers 84 and find 31 satisfies both. Not sure what this means. 31 is certainly not congruent to 2mod4. Why not just stick with 10, which is already congruent to3mod7?

i then use

x congruent 31mod84 and (d)

(84.11=924)

but testing for numbers up to 924 to satisfy both would take forever and so i need to use Euclidean algorithm, and i get confused as i have numbers everywhere am i sposed to being finding 84x+924y=1, my brains frazzled on how to fiind the next number to satisfy equations.thanks

For (d), you want a number x that is congruent to 10mod84 and to 4mod11.

I'd start by subtracting 4, and looking for x–4. This has to be a multiple of 11 that is congruent to 6mod84. So start with 6 and add multiples of 84 until you hit a multiple of 11. You get 6, 90, 194, 258, ... . When you reach a multiple of 11, don't forget to add 4 to get back to x.

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