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Question Number 77015 by aliesam last updated on 02/Jan/20

Commented by MJS last updated on 02/Jan/20

35^2 =1225  335^2 =112225  3335^2 =11122225  ...  (3_n 5)^2 =1_n  2_(n+1)  5  1_(1997)  2_(1998) 5=(3_(1997) 5)^2

$$\mathrm{35}^{\mathrm{2}} =\mathrm{1225} \\ $$$$\mathrm{335}^{\mathrm{2}} =\mathrm{112225} \\ $$$$\mathrm{3335}^{\mathrm{2}} =\mathrm{11122225} \\ $$$$... \\ $$$$\left(\underset{{n}} {\mathrm{3}5}\right)^{\mathrm{2}} =\underset{{n}} {\mathrm{1}}\:\underset{{n}+\mathrm{1}} {\mathrm{2}}\:\mathrm{5} \\ $$$$\underset{\mathrm{1997}} {\mathrm{1}}\:\underset{\mathrm{1998}} {\mathrm{2}5}=\left(\underset{\mathrm{1997}} {\mathrm{3}5}\right)^{\mathrm{2}} \\ $$

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