A number theory problem by Natalia Dcruz
The number of solutions (z,y,x,w,v,u) to
Inspiration - Number Theory Step Up to Level 4 - Set 1
! indicates factorial and x,y,z,w,v and u are non negative integers
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1 solution
Consider (2,2,2,1,3,1) ( By trial and error), since ( 2 ! + 2 ! + 2 ! ) 1 = ( 3 ! ) 1 = 6 . Now if this true then (2,2,2,2,3,2) is a solution, (2,2,2,3,3,3) is solution and so on. So (2,2,2,k,3,k) is a solution where k is a whole number. This is enough to claim that the above equation has infinite solutions