perplexus.info :: Numbers : Y ask about Y ?

Y ask about Y ? (Posted on 2017-04-04)

(i)Y is a positive integer.
(ii) Y-1 is divisible by 5;
(iii) Y is divisible by 2,3,4,6,7,8 and 9.

What is the smallest Y?.

See The Solution Submitted by Ady TZIDON

Rating: 3.0000 (1 votes)

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Explanation to Puzzle Answer

Comment 7 of 7 |

(In reply to Puzzle Answer by K Sengupta)

LCM (2,3,4,6,8,7,9)= 504

Then the Y must be of the form 504*m

Since Y =1 (mod 5) (given), we must have:

504*m = 5n+1

or, -m== 1 ( mod 5)

or, m== 4(mod 4)

So, m=4, 9, 14,...

For m=4, we have Y =504*4=2016

This is a valid solution as 2015 is divisible by 5 and 2016 is divisible by each of

2,3,4,6,8,7,9.

Consequently, the required smallest value of Y is 2016.

Edited on June 9, 2022, 12:58 am

Posted by K Sengupta on 2022-06-09 00:51:09

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