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add external links and wd identifiers
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EgbertRijke committed Dec 6, 2023
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15 changes: 10 additions & 5 deletions src/elementary-number-theory/hardy-ramanujan-number.lagda.md
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Expand Up @@ -20,11 +20,12 @@ open import foundation.unit-type

## Idea

The {{#concept "Hardy-Ramanujan number"}} is the number `1729`. This number is
the second [taxicab number](elementary-number-theory.taxicab-numbers.md), i.e.,
it is the least natural number that can be written as a sum of cubes of positive
natural numbers in exactly two distinct ways. Specifically, we have the
identifications
The
{{#concept "Hardy-Ramanujan number" Agda=Hardy-Ramanujan-ℕ WD="1729" WDID=Q825176}}
is the number `1729`. This number is the second
[taxicab number](elementary-number-theory.taxicab-numbers.md), i.e., it is the
least natural number that can be written as a sum of cubes of positive natural
numbers in exactly two distinct ways. Specifically, we have the identifications

```text
1³ + 12³ = 1729 and 9³ + 10³ = 1729.
Expand Down Expand Up @@ -66,3 +67,7 @@ pr1 (pr2 (pr2 second-sum-of-cubes-decomposition-Hardy-Ramanujan-ℕ)) =
pr2 (pr2 (pr2 second-sum-of-cubes-decomposition-Hardy-Ramanujan-ℕ)) =
refl
```

## External links

- [1729 (number)](<https://en.wikipedia.org/wiki/1729_(number)>) at Wikipedia
9 changes: 8 additions & 1 deletion src/elementary-number-theory/taxicab-numbers.lagda.md
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Expand Up @@ -26,7 +26,9 @@ open import univalent-combinatorics.standard-finite-types

## Idea

The `n`-th {{#concept "taxicab number"}} `taxicab n` is the smallest
The `n`-th
{{#concept "taxicab number" Agda=is-taxicab-number-ℕ WD="taxicab number" WDID=Q1462591}}
`taxicab n` is the smallest
[natural number](elementary-number-theory.natural-numbers.md) `x` such that `x`
is a [sum](elementary-number-theory.addition-natural-numbers.md) of two
[cubes](elementary-number-theory.cubes-natural-numbers.md) in `n`
Expand Down Expand Up @@ -95,3 +97,8 @@ is-taxicab-number-ℕ n x =
## See also

- [The Hardy-Ramanujan number](elementary-number-theory.hardy-ramanujan-number.md)

## External links

- [Taxicab numbers](https://en.wikipedia.org/wiki/Taxicab_number) at Wikipedia
- [Taxicab nubmers](https://oeis.org/A011541) at the OEIS.

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