Determine all
possible integers x that satisfy this equation:
⌊x/2⌋·⌊x/3⌋·⌊x/4⌋·⌊x/5⌋=x3
Reminder: ⌊z⌋ denotes the floor function (the greatest integer less than or equal to z.)
As the LHS is 4th degree we expect it to surpass the RHS even though it starts small. As Charlie points out, x=120 is a somewhat obvious solution. A graph shows two others nearby: https://www.desmos.com/calculator/xxwpqnxzj9
x=(1970050)^1/3 = 125.36
works because the LHS becomes 62*41*31*25=1970050
x=(2050652)^1/3 = 127.046
works because the LHS becomes 63*42*31*25=2050650
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Posted by Jer
on 2022-10-25 10:25:48 |
non-integral answers
