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Let N be a positive integer.  The number N has three digits when expressed in base 7.  When the number N is expressed in base 5, it has the same three digits, in reverse order.  What is N?  (Express your answer in decimal.)

 Jun 19, 2024
 #1
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A7^2 + 7B + C  = C5^2 + 5B + A

 

49A + 7B + C = 25C + 5B + A

 

48A + 2B  = 24C

 

24A + B  = 12C

 

Let B = 0     C =4   and A  = 2

 

A = 2    B = 0  C = 4

 

2047  = 4025  ???

 

2(7)^2 + 0 + 4  = 4(5)^2 + 0 + 2

 

98 + 4  =  100 + 2

 

102  = 102

 

N  = 102

 

cool cool cool

 Jun 19, 2024

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