PP-T1-DS-35

[aqboy[origen]]

Q35

If p and n are positive integers and p > n, what is the remainder when p^2 - n^2 is divided by 15 ?

(1) The remainder when p + n is divided by 5 is 1.

(2) The remainder when p - n is divided by 3 is 1.

請大家幫忙一下~~

另外想請教哪邊有關於"餘數性質"的資料啊?? 這方面特別弱@@

感謝~~~~~

[sunnyblue13s]

p^2 - n^2 =(P+n)(P-n)

if p+n=5k+1....unsufficient...

if p-n=3m+1....unsufficient...

if p+n=5k+1 & p-n=3m+1...still unsufficient....
(if p+n=11, p-n=4....reminder=14; if p+n=6, p-n=7....reminder=12)

(E)