2^391 (mod 391) = 179, not 2 so 391 is definitely a composite number. Scroll down below the puzzle to view its factors.

When I was in elementary school, my sister, Sue, taught me a song she learned in her junior high choir class. I’m not able to find these lyrics on the internet, but as best as I can remember, the words of the song were:

In the woods, in the spring, blooms the lovely wild rose. Every bud waking facing the sun. Hearts of spring, beat on thee, as the light of day grows. Dew drops glisten on you, Wild Rose. Fill the countryside with your lovely fragrance. Sun keeps your petals warm, leaves hide you from harm. Day will break, petals close, close them, oh, so tightly. Cover your beauty from the cool night. Birds, winging, singing through the woodland. Sleep and dream, sleep and dream, sleep and dream.

Print the puzzles or type the factors on this excel file:12 Factors 2015-02-09

- 391 is a composite number.
- Prime factorization: 391 = 17 x 23
- The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 x 2 = 4. Therefore 391 has exactly 4 factors.
- Factors of 391: 1, 17, 23, 391
- Factor pairs: 391 = 1 x 391 or 17 x 23
- 391 has no square factors that allow its square root to be simplified. √391 ≈ 19.774

- Note that 17 + 3 = 20, and 20 + 3 = 23, and (20^2) – (3^2) = 400 – 9 = 391.
- 2(3*20), (20^2) – (3^2), (20^2) + (3^2) makes primitive Pythagorean triple 120-391-409.
- 391-76440-76441 is another primitive Pythagorean triple
- 184-345-391 is [8-15-17] multiplied by 23
- 391-3312-3335 is [17-144-145] multiplied by 23
- 391-4488-4505 is [23-264-265] multiplied by 17

There are lots of recordings of “To A Wild Rose” by Edward Macdowell on YouTube, but I’ve always thought of it as a piano piece and the only lyrics I can locate are totally different to yours.

Like you, I’ve some words from my schooling I’ve never tracked down – we would sing a hymn which contained the memorable couplet: “Each happy morning thou dost give, we have one morning less to live”.

That’s what I noticed when I looked for the lyrics online! The music is familiar to me, but the words going with them certainly are not. Thank you for trying to find them anyway!

“Each happy morning thou dost give, we have one morning less to live”. Such a sobering thought!