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February 24th, 2016, 11:08 PM  #1 
Senior Member Joined: Apr 2010 Posts: 128 Thanks: 0  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 02620 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 24th, 2016 at 11:09 PM. Reason: Change the word prove to EXPLAIN in title. 

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