A number theory problem by madhav srirangan

Number Theory Level 3

How many positive integral values of x ≤ 100 x\leq100 where ( 3 x − x 2 ) (3^{x}-x^{2}) is divisible by 5?


The answer is 20.

Madhav Srirangan by madhav srirangan , 20, India

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1 solution

Code 

1
2
3
 
for x in range(0,101):
    if ((((((3**x)))-(((x**2)))))%(5)==0):
        print (x)

Output 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
 
2
4
16
18
22
24
36
38
42
44
56
58
62
64
76
78
82
84
96
98

No. of outputs

No. of outputs = 20 \boxed{20}

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