MHB What are the ordered pairs for (1+a!)(1+b!) = (a+b)!?

  • Thread starter Thread starter juantheron
  • Start date Start date
juantheron
Messages
243
Reaction score
1
Find all ordered pairs $(a,b)$ for which $(1+a!)(1+b!) = (a+b)!$

where $a,b\in \mathbb{N}$ and $n! = $ factorial on $n$
 
Mathematics news on Phys.org
jacks said:
Find all ordered pairs $(a,b)$ for which $(1+a!)(1+b!) = (a+b)!$

where $a,b\in \mathbb{N}$ and $n! = $ factorial on $n$

Hello.

http://mathhelpboards.com/challenge-questions-puzzles-28/solving-equation-ii-9685.html

Regards.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top