Again 25 = 21

Level pending

How many ordered pairs (x,y) are there such that ( 25 ) x = ( 21 ) y (25)_x=(21)_y where x and y are positive radices and 5 < x < y ≤ 100 5\lt{x}\lt{y}\leq100 .


The answer is 93.

Joji Joseph by Joji Joseph , 27, India

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2 solutions

Mrugesh Joshi
Mar 6, 2014

5+2x=1+2y So, y-x=2 For 5 less than x less than y less or equal to 100, We get x=6,7,8,9,....,98 so, there are 93 pairs

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Nitesh Varshney
Jan 15, 2014

2x+5=2y+1 or y-x=2 if x=6 than y=8 8<=y<=100 total pairs= 100-7 =93

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