Question 1174804: the fields medal the highest scientific award for mathematics is awarded evey 4 years. It was awarded in 2010. the birkhoff prize for applied mathematics is awarded evry 3 years. It was awarded in 2009. What are the first two times when both awards were given in the same year in 21st century?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Edit: I've included the year 2018 as part of the answer after rereading the problem.
The Fields Medal is awarded every 4 years.
The Birkhoff Prize is awarded every 3 years.
With 2010 as a reference point for the Fields Medal, let's write a few numbers that are 4 spaces ahead and behind this reference year.
{..., 1990, 1994, 1998, 2002, 2006, 2010, 2014, 2018, 2022, 2026, 2030, ...}
Do a similar thing for the Birkhoff Prize years. We start at 2009. Add and subtract multiples of 3 to represent possible years the prize is given
{..., 1994, 1997, 2000, 2003, 2006, 2009, 2012, 2015, 2018, 2021, 2024...}
The year marked in red is where the two prizes line up, and also the smallest such year in the 21st century (which starts at the year 2000).
Note how 4*3 = 12 is the LCM of 4 and 3. This tells us that the two awards will line up every 12 years. So 2006+12 = 2018 is the next time the two awards will be given together. To help confirm this, the year 2018 is found in both sets listed above.
Also, note that 2006-12 = 1994 was the last time prior to the 2006 year, is when the two awards lined up. The year 1994 is found in both sets listed above.
These years are when the two awards lined up
{..., 1994, 2006, 2018, ...}
-----------------------------------------------------------------
Answer: The year 2006 and 2018
Answer by ikleyn(52781)  (Show Source):
|
|
|
