# Tag Archives: Patterns

## Patterns with some numbers that have 2 representations as a sum of 2 squares

a,     b,     c                 a,     c,     b,     a a = 1 1157   has 2 representations as a sum of 2 squares: the digits on one side are                     1,     3,     … Continue reading

## Patterns with 1/7

(period 6) Move 7 :       (period 6) Move 4 :       (period 6) Move 1 :       (period 6) Move 8 :       (period 6) Move 5 :       (period 6) … Continue reading

## Patterns-Reversible pairs| (10a + b)^2 + (10x + y)^2 = (10b + a)^2 + (10y + x)^2

By solving the equation I get the following results:   ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ……………………………………. ………………………………… ………………………………… ………………………………… ………………………………… ………………………………… ………………………………… ………………………………… ………………………………… ………………………………… ………………………………… ………………………………… … Continue reading

## When the last d digits of n-digit num3er is n times the first d digits

Posted in Number Puzzles | Tagged | 1 Comment

## Four Consecutive Num3ers: Interesting property

If   A,   B,   C,   D   are four consecutive natural numbers , then     is a factor of the sum     Letâ€™s take, for example,   16,   17,   18,   19 … Continue reading

## Patterns: 4 arbitrary natural numbers

Take four arbitrary natural numbers,   ,   ,     and   . Prove that if use them to find the four numbers   ,   ,     and   ,   which are equal, respectively, to … Continue reading

## Patterns | Integer N, N^2 = x^3 + y^3

To Be Continued

## Patterns| Base-10 integers in pair bases b1 and b2

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## Patterns | Prime Num3ers P of the form P = x^3 – y^3

To find prime numbers having the form x^3 – y^3. Is their DigitSums always 1 or 7?   See:   Cuban prime   http://en.wikipedia.org/wiki/Cuban_prime Digital Root   http://mathworld.wolfram.com/DigitalRoot.html Hint:

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## Patterns – Multiplication