2^ a + 4^b + 8^c = 328

 2^ a + 4^b + 8^c = 328

 2^ a + 2^2^b + 2^3^c = 328

2^ a + 2^2b + 2^3c = 328

{a, 2b, 3c} = {p, q, r} com p ≤ q ≤ r

2^p + 2^q + 2^r = 8 *41

2^p [1 + 2^(q-p)+ 2^(r-p)] = 41 * 2³

2^p = 2³

Assim

p = 3

 [1 + 2^(q-p)+ 2^(r-p)] = 41

2^(q-p)+ 2^(r-3) = 40

2^(q-3) ( 1+ 2^r-q) = 2^3 *(1+2^2)

2^(q-p) = 2^3

q-p = 3

q - 3 = 3

r - q = 2

r - 6 =2

r = 6 + 2

r = 8

p = 3, q = 6, r = 8

{a, 2b, 3c }={p, q, r}={3, 6, 8}

a	2b	3c
8	6	3
6	8	3
3	8	6

a = 8, b = 3 e c = 1

a = 6, b = 4 e c = 1

a = 3, b = 4 e c = 2

q = 3 + 3

q = 6