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What is the largest three-digit integer n that satisfies 55n = 165 (mod 220)?

 
 Sep 13, 2021
 #1
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three digits?

I was going to say 3

 
 Sep 13, 2021
 #2
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55*1=55 mod 220

55*2=110 mod220

55*3=165mod220

55*4=0 mod220

so

55*(4k+3)=165(mod220)

n=4k+3

the biggest three digit n is 999

 
 Sep 14, 2021

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