If you calculate, for m=1,2,3, ...
85^m  (int(85^(m/4)))^4
you get the following:
4
664
82684
0
6287029
1271393704
26172579244
0
32738295586176
246734877110272
9.73675819302912E+015
0
Not surprising, every 4th one is zero, whenever m is 0 mod 4. So the only hope of the original equation being true is for an 'm' that is 1 mod 4. And for m=1, this one works perfectly. But as m gets larger, the differences are much too large to ever be as small as 4.
Not as mathematically rigorous as I'd like, but ...

Posted by Larry
on 20201013 10:52:10 