MATH 267求解！！！

gedn01

267. If n is an integer between 10 and 99 and n is divisible by 7, the remainder is 3, is n< 80?
1) When n is divided by 5, the remainder is 0->不充分
2) When n is divisible by 3, the reminder is 0
Inclusive ?

n = 7m + 3

from 1) à n = 5k à n = 35t + 10, t = 0, 1, 2, 3, … sonot A

from 2) à n = 3s à n = 21a + 24a = 0, 1, 2, 3, …sonot B

union à n = 35t + 10 , n = 3s à n = 105 k + 45 在 10 到 99 只有45满足条件 so C
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其中10,24,45分别是怎么算出来的？谢谢

jayhhh

同問

red926

令n=7x+3   , 10<7x+3<99推出  2<=x<=13再想如果要被5整除尾数为0或5那么7x的尾数只能为2或7 那么x只能去11和6~~这个数还要还要被3整除x就只能为6了。。。可能我想的比较复杂T T~~