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\(\text{Suppose $a$ is an integer such that $0 \le a \le 14$, and $235935623_{74}-a$ is a multiple of $15$. What is $a$? }\)

 Jul 31, 2019
 #1
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+1

If we convert 235935623 from base 74 to base 10 = 1,835,684,416,755,975. This number is ALREADY  a multiple of 15, which means that a = 0. 

 Jul 31, 2019
 #2
avatar+106963 
+1

I just lost a very time consuming answer. But yes that number mod 15 is 0 so  a must be zero.

Here is the short version.

 

This is a very weirdly presented question.  That number is base 74 (very strange) but 15 is base 10

 

Use the fact that     74 mod 15 = -1

 

So when mod 15 of that number is taken we get 

 

2-3+5-9+3-5+6-2+3 = 0 

 

In other words that number is already a multiple of 15 (base10)  so a = 0

 Aug 1, 2019

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