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 A^2 = B^3 + C^3
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 smallest integer whose first n multiples all contain a 3
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Monthly Archives: March 2015
Triangular Num3ers T(n)^4 = ((1^5 + 2^5 + … + n^5) + (1^7 + 2^7 + … + n^7))/2
…………………….. …………………….. Prove for all n positive integers that
Num3er 315
315 has 12 divisors: 1 3 5 7 9 15 21 35 45 63 105 315 Sum of divisors: 624 … Continue reading
Is the Triangular number T(11…11) (2n ones) always a palindromic number?
Is the triangular number (2n ones) always a palindromic number?
Triangular number n^3 = T(n)^2 – (T(n) – n)^2
………………………… ………………………… …………………………
Why is every 4th power > 1 the sum of two triangular numbers?
Explain this …………………. ………………….
System of equations: x^(x+y) = y^12 and y^(x+y) = x^3
Hint: the solutions are: Solve analytically
Equation x^x = (xy)^(x+y)
x and y are positive integers. Is there a solution to Paul found: ……….
Num3er 144 – Remarkable Property
Each of its first 50 multiples differs from the first perfect square (S) by a perfect square, for the exceptions of The pattern breaks here: Find another example… …then show that, for any positive integer … Continue reading
Sets of 3 triangular numbers in geometric progression
In a geometric progression, any three consecutive terms a, b and c will satisfy the following equation: common ratio = 6, , , , common ratio = 35/6 … Continue reading