Question

Determinați numărul abbc dacă abbc=d^2×aad.​

Answer 1

$\displaystyle\bf\\\textbf{Avem o singura ecuatie si 4 necunoscute.}\\\textbf{O voi rezolva prin incercari.}\\\\\overline{abbc}=d^2\times\overline{aad}\\\\\frac{\overline{abbc}}{d^2}=\overline{aad}\\\\ a\neq0\\\textbf{Un numar de 4 cifre impartit la un patrat perfect }\\\textbf{este egal cu un numar de 3 cifre.}\\\textbf{Dezulta ca }~d^2~\textbf{ poate avea una sau/si 2 cifre.}\\d^2=1^2~~nu~este~acceptat.\\d^2\in\{2^2;~3^2;~4^2;~5^2;~6^2;~7^2;~8^2;~9^2\}\\d^2\in\{4;~9;~16;~25;~36;~49;~64;~81\}$

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$\displaystyle\bf\\\frac{\overline{abbc}}{d^2}=\overline{aad}\\\\Alegem:\\ a=1;~2;~3;~...~9\\b=0;~1;~2;~...~9\\\textbf{c ales astfel ca }abbc~\vdots~pp\\\\\frac{1000}{2^2}=250~~Nu~e~bun\\\\\frac{1004}{2^2}=251~~Nu~e~bun\\\\\frac{1008}{2^2}=252~~Nu~e~bun\\\\\frac{1008}{3^2}=112~~Nu~e~bun.~~113~era~bun.\\\\4^2~prea~mare\\\\\frac{2000}{2^2}=500~~Nu~e~bun\\\\\frac{2004}{2^2}=501~~Nu~e~bun\\\boxed{\bf\frac{2007}{3^2}=223~~CORECT}\\\boxed{\bf~a=2;~b=0;~c=7;~d=3}$

Am continuat cautarile pana la a = 9; b = 9; c = 9; d = 9,

dar nu am mai gasit alte solutii.