2-a-2-b-2-c-2-d-57-find-a-b-c-d-a-b-c-d-and-a-b-c-d-are-positive-integers-

Question Number 113372 by Aina Samuel Temidayo last updated on 13/Sep/20

2^{a} + 2^{b} + 2^{c} + 2^{d} = 57, find a + b + c + d .

a \neq b \neq c \neq d and a, b, c, d are positive

integers .

Commented by udaythool last updated on 13/Sep/20

\dots is there any restrictions on

a, b, c, d ?

If a, b, c, and d are integers then

it has a unique solution,

otherwise infinitely many

solutions \dots

Commented by Aziztisffola last updated on 13/Sep/20

\frac{57}{2} \Rightarrow q = 28 & r = 1

\frac{28}{2} \Rightarrow q = 14 & r = 0

\frac{14}{2} \Rightarrow q = 7 & r = 0

\frac{7}{2} \Rightarrow q = 3 & r = 1

\frac{3}{2} \Rightarrow q = 1 & r = 1

57 = {(111001)}_{2} = 2^{0} + 2^{3} + 2^{4} + 2^{5}

\Rightarrow 0 + 3 + 4 + 5 = 12

Answered by bemath last updated on 12/Sep/20

2^{5} + 2^{4} + 2^{3} + 2^{0} = 57

\Rightarrow a + b + c + d = 12

Commented by Aina Samuel Temidayo last updated on 12/Sep/20

Yea .