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The number t = 1 + 2 + 1 + 2 + ... + n is called the nth triangular number (so called because t, dots may be inserted in an orderly fashion in an equilateral triangle; the fourth triangular number is familiar to bowlers). Some triangular numbers are also squares (which means that the dots may be rearranged into a square), for example, tg = 62, 149 = 35². Show that there are infinitely many numbers that are simultaneously triangular and square.

The number t = 1 + 2 + 1 + 2 + ... + n is called the nth triangular number (so called because t, dots may be inserted in an orderly fashion in an equilateral triangle; the fourth triangular number is familiar to bowlers). Some triangular numbers are also squares (which means that the dots may be rearranged into a square), for example, tg = 62, 149 = 35². Show that there are infinitely many numbers that are simultaneously triangular and square.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7. The number t₁ = 1 + 2 + +n is called the nth triangular number (so called because t, dots may be inserted in an orderly fashion in an equilateral triangle; the fourth triangular number is familiar to bowlers). Some triangular numbers are also squares (which means that the dots may be rearranged into a square), for example, tg = 6²,149 = 35². Show that there are infinitely many numbers that are simultaneously triangular and square. this is a number theory problem
Transcribed Image Text:7. The number t₁ = 1 + 2 + +n is called the nth triangular number (so called because t, dots may be inserted in an orderly fashion in an equilateral triangle; the fourth triangular number is familiar to bowlers). Some triangular numbers are also squares (which means that the dots may be rearranged into a square), for example, tg = 6²,149 = 35². Show that there are infinitely many numbers that are simultaneously triangular and square. this is a number theory problem
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