crossnumber #8
 

A challenging puzzle I found mentioned on [URL]https://blogs.ams.org/blogonmathblogs/[/URL] :

[URL]http://chalkdustmagazine.com/regulars/crossnumber/prize-crossnumber-issue-08/[/URL]

[QUOTE=Till;499914]A challenging puzzle I found mentioned on [URL]https://blogs.ams.org/blogonmathblogs/[/URL] :

[URL]http://chalkdustmagazine.com/regulars/crossnumber/prize-crossnumber-issue-08/[/URL][/QUOTE]
a few things.
[SPOILER]9D,36A,20D,3D,4D,22D,8D,26D,23A,5D, and 6D have to all be 2 mod 5 and 6 mod 7 ( so 27 mod 35)
21A is 257
16D and 3A both show 18A<72, if different 18A<69
1A is surrounded by numbers that only have 2's and 3's as factors because n^2-1=(n-1)*(n+1)
[/SPOILER]

[QUOTE=science_man_88;499925]a few things.
[SPOILER]9D,36A,20D,3D,4D,22D,8D,26D,23A,5D, and 6D have to all be 2 mod 5 and 6 mod 7 ( so 27 mod 35)
21A is 257
16D and 3A both show 18A<72, if different 18A<69
1A is surrounded by numbers that only have 2's and 3's as factors because n^2-1=(n-1)*(n+1)
[/SPOILER][/QUOTE]

I found this one MUCH easier than one I did a few months ago....only took me a few hours off and on.

Now lets hope I submitted the right sum

2 hints:
34A; Proth Numbers
14D: Triperfect number