Prove the transitivity of modular congruence. That is, prove that for all integers a,b,c, and n with n > 1, if a = b(mod n) and b = c(mod n) then a = c(mod n).

tricotasu 2021-01-31 Answered
Prove the transitivity of modular congruence. That is, prove that for all integers a,b,c, and n with n > 1, if a=b(mod n) and b=c(mod n) then a=c(mod n).
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firmablogF
Answered 2021-02-01 Author has 92 answers
The transitivity of modular congruence is that for all integers a, b, c and n with n > 1, if ab(mod n) and bc(mod n) then ac(mod n)
If ab(mod n) and bc(mod n), then there exists integers k and k’ such that,
qb=nk
bc=nk
Adding these two equations yields
ac=n(k+k)
where, k +k’ is an integer.
And so ac(mod n)
Conclusion:
The theorem of transitivity of modular congruence is proved.
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