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Powerful Parade (Posted on 2023-09-03)

If
4^a + 5^b + 6^c = 8^8 + 9^9 + 10^10

then what is the sum S=a+b+c (each a positive integer)?

No Solution Yet Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

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Puzzle Answer

Comment 5 of 5 |

If + signs are replaced with *, then:

4^a*5^b* 6^c = 8^8*9^9*10^10

=-> 4^a*5^b*6^c = 8^8*3^18*+10^10 = 4^8* 2^8*5^10*2^10*3^18 =

= 4^8*5^10*2^18*3^18 = 4^8*5^10*6^18

Thus, (a,b,c) = (8,10,18)

Then, S = a+ b+c = 8+10+18 = 36

Edited on September 4, 2023, 3:49 am

Posted by K Sengupta on 2023-09-04 03:48:29

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