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Algebra Level 4

2 a + 2 b + 2 c + 2 13 = 2 d \large { 2 }^{ a }+{ 2 }^{ b }+{ 2 }^{ c }+{ 2 }^{ 13 }={ 2 }^{ d }

Given that a , b , c , d a,b,c,d are positive integers that satisfy the above equation.Then what is the maximum value of a + b + c + d a+b+c+d ?


The answer is 58.

Porames Vattanaprasan by Porames Vattanaprasan , 21, Thailand

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1 solution

We know that 2 x + 2 x = 2 x + 1 { 2 }^{ x }+{ 2 }^{ x }=2^{ x+1 } From the problem 2 a + 2 b + 2 c + 2 13 = 2 d { 2 }^{ a }+{ 2 }^{ b }+{ 2 }^{ c }+{ 2 }^{ 13 }={ 2 }^{ d } for the maximum value of a, b, c, d you should write in 2 13 + 2 a + 2 b + 2 c = 2 d { 2 }^{ 13 }+{ 2 }^{ a }+{ 2 }^{ b }+{ 2 }^{ c }={ 2 }^{ d } where a = 13, b = 14, c = 15 and d = 16 so a+b+c+d = 13+14+15+16 = 58

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Did the same way.

Niranjan Khanderia - 5 years, 8 months ago

well done sir

Kaustubh Miglani - 5 years, 8 months ago

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