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February 25th, 2016, 12:08 AM   #1
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How to EXPLAIN? Arithmetic Progression unique digit value

Given the formula

$\displaystyle y(y+1)$
for all positive integer including 0 , why the digit value will never end up in 4 or 8?

i tried brute force and notice that
0x1=0-------------+0
1x2=2-------------+2
2x3=6-------------+4
3x4=12------------+6
4x5=20------------+8
5x6=30------------+10
6x7=42------------+12
7x8=56------------+14
8x9=72------------+16

the increment value is always +2 such that 0,2,4,6,8,10,12.....

and if we group the increment value together , we get 2+8=10 , 4+6=10

which is a looping 10 rendering the digit value of y(y+1) keep looping at 0-2-6-2-0

But how am i suppose to explain WHY y(y+1) it can never end up 4 or 8?

Is there any unique characteristics to number which has digit 4 or 8? Such that it can never be written in the form of y(y+1).

Last edited by rnck; February 25th, 2016 at 12:09 AM. Reason: Change the word prove to EXPLAIN in title.
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