When positive integer n isdivided by 3, the remainder is 2; and when positive integer t is divided by 5,the remainder is 3. What is theremainder when the product nt is divided by 15 ?
from (1): since (n-2=3a) is divisible by 5, a=5a'
therefore: nt= 15ab+45a'+ 10b +6,
15ab and 45a' can be divided by 15, but we are not sure about 10b. Insufficient
from (2): since (t=5b+3) is divisible by 3, b=3b'
therefore: nt=15ab+9a+30b' +6
15ab and 30b' can be divided by 15, but we are not sure about 9a. Insufficient
Together (1) and (2)
nt=15ab+45a' +30b' +6.
15ab, 45a' and 30b' can be divided by 15, therefore remainder must be 6.
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发表于 2015-3-23 22:29:30
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