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Take from Joseph Rotman's "A First Course in Algebra: with applications":

The smallest value of $n$ for which the function $f(n) = 991n^2 + 1$ is a perfect square is

$$ n = \mbox{12,055,735,790,331,359,447,442,538,767}. $$

(This number is approximately $50$ times larger than the square of the United States' national debt!)

Update: As of August 23rd, 2014, the number is now just over $38$ times larger than the square of the United States' National debt.

On a similar note, the smallest value of $n$ such that the function $g(n) = 1,000,099n^2 + 1$ is a perfect square has $1116$ digits.

Take from Joseph Rotman's "A First Course in Algebra: with applications":

The smallest value of $n$ for which the function $f(n) = 991n^2 + 1$ is a perfect square is

$$ n = \mbox{12,055,735,790,331,359,447,442,538,767}. $$

On a similar note, the smallest value of $n$ such that the function $g(n) = 1,000,099n^2 + 1$ is a perfect square has $1116$ digits.

Take from Joseph Rotman's "A First Course in Algebra: with applications":

The smallest value of $n$ for which the function $f(n) = 991n^2 + 1$ is a perfect square is

$$ n = \mbox{12,055,735,790,331,359,447,442,538,767}. $$

(This number is approximately $50$ times larger than the square of the United States' national debt!)

On a similar note, the smallest value of $n$ such that the function $g(n) = 1,000,099n^2 + 1$ is a perfect square has $1116$ digits.

Take from Joseph Rotman's "A First Course in Algebra: with applications":

The smallest value of $n$ for which the function $f(n) = 991n^2 + 1$ is a perfect square is

$$ n = \mbox{12,055,735,790,331,359,447,442,538,767}. $$

(This number is approximately $50$ times larger than the square of the United States' national debt!)

Update: As of August 23rd, 2014, the number is now just over $38$ times larger than the square of the United States' National debt.

On a similar note, the smallest value of $n$ such that the function $g(n) = 1,000,099n^2 + 1$ is a perfect square has $1116$ digits.

Take from Joseph Rotman's "A First Course in Algebra: with applications":

The smallest value of $n$ for which the function $f(n) = 991n^2 + 1$ is a perfect square is

$$ n = 12,055,735,790,331,359,447,442,538,767. $$

(This number is approximately $50$ times larger than the square of the United States' national debt!)

On a similar note, the smallest value of $n$ such that the function $g(n) = 1,000,099n^2 + 1$ is a perfect square has $1116$ digits.

Take from Joseph Rotman's "A First Course in Algebra: with applications":

The smallest value of $n$ for which the function $f(n) = 991n^2 + 1$ is a perfect square is

$$ n = \mbox{12,055,735,790,331,359,447,442,538,767}. $$

(This number is approximately $50$ times larger than the square of the United States' national debt!)

On a similar note, the smallest value of $n$ such that the function $g(n) = 1,000,099n^2 + 1$ is a perfect square has $1116$ digits.