What does a ≡ b (mod n) mean? Basic Modular Arithmetic, Congruence

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Thanks for the refresher. I hardly understood this when getting my undergrad degree and now that im working on my masters it came back to haunt me 🤣

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10 congruent 14(mod 4) , or 10 = k*4 + 14. So by your example 10 congruent 2(mod 4) and 10 congruent 14 (mod 4) are equivalent statements?

I hope this comment will be noticed. Can b be greater than the value of n? Thank you in advance to the person who will answer✨✨

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(by wikipaedia) Actually, the first claim is the most correct one, same remainder when a and b are divided by n,
a = kn + r, b = jn + r then we have a - b = (k-j)n + 0 which means that n | a - b (the last claim). If we add b to both side,
a = Kn + b by setting K = k - j.

edit: depends on variables to choose the most suitable one.

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I'm really confused😢

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summary: a = b mod m is known ads congrunce relation where a divides m and b divides m with same remainder and a is some constant times *m +b

Can I solve for i in this equation?
(n-i) % (m+1) = 0

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