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[TEX]b = 100 . . . 05 = 100 . . . 0 - 1 + 6 = 99 . . . 9 + 6 = 9a + 6[/TEX]
[TEX]\Rightarrow ab + 1 = a(9a + 6) + 1 = 9a^2 + 6a + 1 = (3a + 1)^2[/TEX]
[TEX]\Rightarrow \sqrt{ab+1}=\sqrt{(3a+1)^2}=3a+1 \in N[/TEX]
 
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