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A147520 a(n) = Smallest number x such that Euler Polynomial x^2 + x + 41 is divisible by 41^n.

%I A147520 #10 Apr 09 2018 22:55:01
%S A147520 0,40,1721,139563,14268368,1636255182,6386359423,1953929098233,
%T A147520 149759650255065,1814531956108700,243422399538851918,
%U A147520 9662500171353620019,122479951673184550424,12148820281768361731597,177497315692809432279207,14173382150616650630276616,1225594969529024683212496795
%N A147520 a(n) = Smallest number x such that Euler Polynomial x^2 + x + 41 is divisible by 41^n.
%C A147520 For values of x^2 + x + 41, see A147521. For values (x^2 + x + 41)/(41^n), see A147522.
%C A147520 By Hensel's lemma, x^2 + x + 41 has two roots mod 41^n; their sum == -1 mod 41^n. Thus 0 <= a(n) < 41^n/2. - _Robert Israel_, Apr 09 2018
%H A147520 Robert Israel, <a href="/A147520/b147520.txt">Table of n, a(n) for n = 1..620</a>
%p A147520 f:= n -> min(map(t -> rhs(op(t)), [msolve(x^2+x+41, 41^n)])):
%p A147520 map(f, [$1..30]); # _Robert Israel_, Apr 09 2018
%t A147520 a = {}; Do[x = 0; While[Mod[x^2 + x + 41, 41^n] != 0, x++ ]; AppendTo[a,x];Print[{n, x, x^2 + x + 41, (x^2 + x + 41)/41^n}], {n, 1, 6}];a (* _Artur Jasinski_ *)
%Y A147520 Cf. A145292, A145293, A145294, A147520, A147521, A147522.
%K A147520 nonn
%O A147520 1,2
%A A147520 _Artur Jasinski_, Nov 06 2008
%E A147520 More terms from _Robert Israel_, Apr 09 2018