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5/2/20 Daily Magic Spells

 
 
Picture of Ayu Kira
5/2/20 Daily Magic Spells
by Ayu Kira - Sunday, May 3, 2020, 10:04 AM
 

I found an error in solution for 5/2/20 Daily Magic Spells. It says,"The numbers that leave a remainder of 10 when we use them to divide 100 are 15, 30, 45 and 90."

18 is missing!

My solution:

100 ≡ 10 (mod n), 100 ≡2 (mod n-1)

⇔n丨90, n-1丨98

n are factors of 90 larger than 10: 15, 18, 30, 45, 90

Among them, the only n that satisfies n-1丨98 is 15

∴n=15




 
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Re: 5/2/20 Daily Magic Spells
by Areteem Professor - Monday, May 4, 2020, 10:28 AM
 

Thank you for your message, Ayu!

You are correct, 18 is also one of the numbers that leave remainder 10 we used to divide 100. It is now added to the solution.