perplexus.info :: Just Math : Four Powers

Four Powers (Posted on 2023-08-10)

8^a+2^b+16^c+2^d=660

Find (a,b,c,d)

No Solution Yet Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Puzzle Solution

Comment 2 of 2 |

Substituting a=3, and b=7, we

have::

16^c + 2^d = 660-512-128 = 20

=> c= 1, and d= 2

Thus, (a,b,c,d) = (3, 7, 1,2) is a solution.

In a similar vein, taking a=3, and d=7, we would have got:

2^b+16^c,=20, so that:

b =1, c=2

Therefore: (a,b,c,d) = (3,2,1,7) is another solution.

Consequently, (a,b,c,d) = ( 3, 7, 1, 2) , (3, 2, 1,7) are the.possible integer solutions to the given puzzle.

Edited on September 12, 2023, 12:05 am

Posted by K Sengupta on 2023-08-10 08:40:06

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info