if (x:41) ---- remainder=41,
if ((x^-1) : 82) --- remainder=81
if ((x^4-1) : 164) --- remainder=163
The minimal value of x is ....?

Question

if (x:41) ----> remainder=41,
if ((x^-1) : 82) ---> remainder=81
if ((x^4-1) : 164) ---> remainder=163
The minimal value of x is ....?

anonymous · Answer

if ((x^2-1) : 82) ---> remainder=81  ?

anonymous · Answer

yes..

anonymous · Answer

oh sorry, the first if (x:41) ----> remainder=40

anonymous · Answer

i think its impossible 

if (x:41) ----> remainder=40   then  x=41k+40  k=0,1,2,... 

we have 2 cases   
case I) k=2m+1  m=0,1,2,...
then x=41(2m+1)+40=82m+81
so (x^2-1=(x-1)(x+1)=(82m+80)(82m+82):82) ----> remainder=0


case II) k=2m  m=0,1,2,...
then x=41(2m)+40=82m+40
so (x^2-1=(x-1)(x+1)=(82m+39)(82m+41):82) ----> remainder=39*41 or 41

anonymous · Answer

let me know what is your idea