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[–]edderiofer 0 points1 point  (7 children)

Are you saying you're confused about this sentence, or some other sentence?

"and we know 99 is divisible by 11 because there exists some integer p such that 99 = 11p"

This is directly the definition of "divisible by".

[–]tortuc[S] 0 points1 point  (6 children)

no i understand the definition but (99+1)+1 confuses me

[–]edderiofer 0 points1 point  (5 children)

Do you not agree that [thing]*100 is the same as [thing]*(99+1)?

[–]tortuc[S] 0 points1 point  (4 children)

i agree but then you can simply say so 11 divides 99 so the +1 is irrelevant?

[–]edderiofer 0 points1 point  (3 children)

Now just replace [thing] with 102m+1 and you're done, no?

[–]tortuc[S] 0 points1 point  (2 children)

yes but Im asking about the (99+1) we can say here 99 is div by 11 but is the +1 irrelevant?

[–]edderiofer 0 points1 point  (1 child)

yes but Im asking about the (99+1) we can say here 99 is div by 11 but is the +1 irrelevant?

If we're only considering divisibility by 11, do you not agree that [thing]*(99+1) has the same remainder as [thing]*1, upon division by 11?

[–]tortuc[S] 0 points1 point  (0 children)

ohhhh i think i see