Question

can somebody help me?

Answer 1

N is an even 3-digit number such that the last 3 digits of N square are N itself. What is the value of N?

Answer 2

hmm, just thinking but ...\[100a+10b+c=2n\]
\[(100a+10b+c)^2=4n^2\]

100a+10b+c
100a+10b+c
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10000a^2 + 1000ab + 100ac
1000ab + 100b^2 +10bc
100ac +10bc +c^2
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\[10000a^2 ~~~~+ 2000ab~~~ + 200ac ~~~~+100b^2~ +20bc ~+c^2\]

Answer 3

if we subtract 2n from 4n^2, we should end up with some:

100000x +10000y+1000z

Answer 4

\[10000a^2-100a+100b^2-10b+c^2-c+2000ab + 200ac +20bc=4n^2-2n\]
\[100(100a^2-a)+10(10b^2-b)+(c^2-c)+20(100ab + 10ac +bc)=2n(2n-1)\]
still just thinking ...