Solutions

Calculus Level 4

Let 2 a 1 + 3 a 2 + 5 a 3 + 7 a 4 + 9 a 5 2^{a_1} + 3^{a_2} + 5^{a_3} + 7^{a_4} + 9^{a_5} is divisible by 4 , where a 1 , a 2 , . . . . . . . , a 5 a_{1} , a_{2} , ....... , a_{5} are digits. If the number of solutions of ( a 1 , a 2 , a 3 , a 4 , a 5 ) (a_{1} , a_{2} , a_{3} , a_{4} , a_{5}) is P , then

P 9 X 5 4 = \frac{P}{9 X 5^{4}} =


The answer is 8.

U Z by U Z , 24, Guyana

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1 solution

Ar Agarwal
Oct 27, 2014

The following python script does the magic: 

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def factors_set():
    factors_set = ((i,j,k,l,m) for i in range(0,10) for j in range(0,10) for k in range(0,10) for l in range(0,10) for m in range(0,10))
    for factor in factors_set:
        yield factor

def linear_combination():
    count = 0
    for factors in factors_set():
            if((2**factors[0]+3**factors[1]+5**factors[2]+7**factors[3]+9**factors[4])%4==0):
                count = count+1
    print (int(count/(9*5**4)))

linear_combination()

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Someone please post a solution without programming...

Anik Mandal - 5 years, 3 months ago

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