help

[inner surge]

plz help me with this one

[mint flume]

2

[inner surge]

can anyone explain this more clearly i am relatively new to this concept

[woven vigil]

do they mean divided instead of divisible?

divide is a verb, divisible is an adjective

[errant tiger]

i think it means divided

[woven vigil]

here is an idea:

find an n such that 2^n divided by 11 has remainder 1

oh look

2^10 divided by 11 has remainder 1

so you can say 2^(126930) = (2^10)^12693 which is congruent mod 11 to 1^12693 = 1

Do you know why a congruent to b implies a^n is congruent to b^n?

[inner surge]

so for 3^30001 / 26 we can t do that , can we ?

[inner surge]

not really

[woven vigil]

notice 3^3 = 27 which is congruent to 1 mod 26

3^(30001) = 3*(3^3)^10000 congruent mod 26 to 3*1^10000 = 3

Do you know that a congruent to b implies that a + n congruent to b +n?

let's just use ~ for congruence symbol?

a~b (mod m) => a+n ~ b+n

Did you know this^

or this? a~b (mod m) => an ~ bn (mod m)

[fallow island]

2^5 = 32
we can say that
2^5 ≡ -1(mod 11) since 32/11 will give remainder -1
now it is a property of mod that if u can raise the same power to both sides
(2^5)^25386 ≡ (-1)^25386(mod 11)
= 2^126930 ≡ 1(mod11)

so remainder is 1