Waste less time on Facebook — follow Brilliant.
×

Find the simplest way to show that there exist positive integers \(x,y,z\) that satisfy the equation \(29x +30y+31z=366366\).

Note by Pi Han Goh
1 year, 9 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

Number of months with \(29 , 30\) and \(31\) days in \(1001\) leap years. Sudeep Salgia · 1 year, 9 months ago

Log in to reply

@Sudeep Salgia Wow that's quick! Pi Han Goh · 1 year, 9 months ago

Log in to reply

@Pi Han Goh Thanks. Sudeep Salgia · 1 year, 9 months ago

Log in to reply

@Sudeep Salgia amazing ! Karan Siwach · 1 year, 9 months ago

Log in to reply

@Sudeep Salgia Cool observation Sir! Nihar Mahajan · 1 year, 9 months ago

Log in to reply

@Sudeep Salgia Genius! Archit Boobna · 1 year, 9 months ago

Log in to reply

@Sudeep Salgia awesome... Karan Shekhawat · 1 year, 9 months ago

Log in to reply

Take \(x=1\) and by Chicken McNugget there exists \(y,z\) such that \(30y+31z=366337\).

That's the most straightforward way that immediately solves the problem as far as I know. Daniel Liu · 1 year, 9 months ago

Log in to reply

@Daniel Liu But Chicken McNugget didn't explicitly say that \(y,z\) are positive. Pi Han Goh · 1 year, 9 months ago

Log in to reply

@Pi Han Goh It does; or else it would just degenerate to Bezout's Identity. Daniel Liu · 1 year, 9 months ago

Log in to reply

@Daniel Liu OH wait it does! Silly me! Thanks! I've found the second simplest solution. Yay! Pi Han Goh · 1 year, 9 months ago

Log in to reply

Comment deleted Apr 15, 2015

Log in to reply

@Karthik Venkata Note that I'm looking for positive integers \(x,y,z\) not integers \(x,y,z\). Pi Han Goh · 1 year, 9 months ago

Log in to reply

Comment deleted Aug 14, 2015

Log in to reply

@Swapnil Das How is this related to the question? Pi Han Goh · 1 year, 9 months ago

Log in to reply

x=3955;y=4078;z=4171; Ovi Khan · 1 year, 8 months ago

Log in to reply

x=3955;y=4078;z=4171 Ovi Khan · 1 year, 8 months ago

Log in to reply

see if HCF of 29,30,31 divides 366366 completely Saket Sharan · 1 year, 9 months ago

Log in to reply

@Saket Sharan Won't HCF of \(29\), \(30\) and \(31\) be \(1\)? Arulx Z · 1 year, 8 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...