(c)^(ba)=1679616 find a+bxc?

若不限定 a , b , c 為正整數, 則有無限多解.

若限定 a , b , c 為正整數 :
c^(ab) = 1679616 = 2^8 * 3^8 = 6^8 = 36^4 = 1296^2

(1)
c = 6
ab = 8
( a, b ) = ( 1 , 8 ) = ( 2 , 4 ) = ( 4 , 2 ) = ( 8 , 1 )
a + bc = 49 , 26 , 16 , 14

(2)
c = 36
ab = 4
( a , b ) = ( 1 , 4 ) , ( 2 , 2 ) , ( 4 , 1 )
a + bc = 145 , 74 , 40

(3)
c = 1296
ab = 2
( a , b ) = ( 1 , 2 ) , ( 2 , 1 )
a + bc = 2593 , 1298

(4)
c = 1679616
a = b = 1
a + bc = 1679617

Ans :
若不限定 a , b , c 為正整數, 則有無限多解.

若限定 a , b , c 為正整數, 則有 10 個可能解 :
14 , 16 , 26 , 40 , 49 , 74 , 145 , 1298 , 2593 , 1679617