2^x-41
 

Are 8=x and 36=x the only integer values such that 2^x-41 is divisible by 215?

[QUOTE=enzocreti;506547]Are 8=x and 36=x the only integer values such that 2^x-41 is divisible by 215?[/QUOTE]

No. For example:

[CODE]n=215;ph=eulerphi(n);e=8+ph*2^1000;r=Mod(2,n)^(e)-41;if(r==0,print(e))
*** _^_: Warning: Mod(a,b)^n with n >> b : wasteful.
1800134460072929099193354082420803041743160083665296460505500652462189765889892685788573276410369041654359050501489286666314404079963087593245409032549360567061007386170470805550740533650478351835496302601711807797241766132922992949939811382940946569647961008251339084166952211717640896988650552235655176[/CODE]


For those values less than or equal to eulerphi(215):

[code]
n=215;ph=eulerphi(n);for(k=1,ph,r=Mod(2,n)^(k)-41;if(r==0,print(k)))
8
36
64
92
120
148
[/code]