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Number of (4n-3)-digit 4th powers in carryless arithmetic mod 10.
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%I #16 Feb 13 2024 02:59:22

%S 3,24,228,2256,22512,225024,2250048,22500096,225000192,2250000384,

%T 22500000768,225000001536,2250000003072,22500000006144,

%U 225000000012288,2250000000024576,22500000000049152,225000000000098304,2250000000000196608,22500000000000393216

%N Number of (4n-3)-digit 4th powers in carryless arithmetic mod 10.

%D J. Y. Lee and J.-L. Kim, Powers, Pythagorean triples, and Fermat's Last Theorem in carryless arithmetic mod 10, preprint, April, 18, 2013.

%H Jon-Lark Kim, <a href="http://maths.sogang.ac.kr/jlkim/preprints.html"> Preprints</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-20).

%F a(k) = (1/4)*{9* 10^(k-1) - 2^(k-1)} + 2^(k-1).

%F a(n) = 12*a(n-1)-20*a(n-2). G.f.: -3*x*(4*x-1) / ((2*x-1)*(10*x-1)). - _Colin Barker_, May 11 2013

%e For k=1, there are three one-digit 4th powers: 1^4=9^4=3^4=7^4=1, 2^4=8^4=4^4=6^4=6, 5^4=5.

%Y Cf. A169963

%K nonn,base,easy

%O 1,1

%A _Jon-Lark Kim_, Apr 28 2013

%E More terms from _Colin Barker_, May 11 2013