Fei Fei Math Q82

[JS]

82、X=K^4，K是正整数，X被32除后余数是0。问K被32除，余数可能是：
(1)2 (2)4 (3)6
Answer: (2)
X=K^4=32A=2^4 * 2A
因为K是正整数>>>2A最小为16>>>K^4=2^4*2^4m 其中m>=1
>>>K/32=2^(m+1) , m>=1>>>余数为4,8,16…


I am really sorry, another stupid question here. I cant even understand the explaination. please help me again!

[freshmanduke]

k是4的倍數
因為k^4可被32除盡
若k為2 => k^4=16無法被除進 反之k=4 K^4= 4^4 可被32除盡
因此可知 k=4.8.12.16.........
推出k除32其餘數位4.8.12.16......
=>the answer is (2) 4.

[JS]

Thx again Duke for the rescue!! very much appreciated!

[freshmanduke]

you're welcome,JS!