### Today’s Puzzle:

Reading a table is an important mathematical skill. Can you read names from a table even if the table is written in a different language? Note: in Hungary, the surnames are written before the given names.

Debreczeni Eszter was born on 23 February 1855. I know this because that was the date written by the minister on her church’s marriage index.

Today’s puzzle: Look at this table of baptisms and determine the names of Debreczeni Eszter’s parents.

If like me, you quickly determined from entry 79 that Debreczeni Eszter was indeed born on February 23 and baptized on March 28, and her parents’ names were Debreczeni János and Rácz Erzsébet, you will feel quite confused when you look at her 1876 marriage record:

Her father’s name was Debreceni Sándor? What? The birth year of 1855 would be right for a 20-year-old marrying in January of 1876, but when I looked for her on FamilySearch, I didn’t find anyone with her name with that father’s name. Did she lie about her age when she married? Did the minister get it wrong on either the marriage record or the marriage index? She was a member of the Reformed Church when she married, but perhaps she was Lutheran or Jewish when she was born? (Those records haven’t been indexed yet.)

I looked at the marriage index again.

You can see their entry on the top by the date jan. 5. As you can see, the minister did not write in dates of birth for all those getting married. Did he get this 1855-ii-23 birthdate wrong?

Knowing that if she lived into the 20th century, there was a good chance the names of her husband as well as both of her parents would appear on her death record, I looked through years of not-yet-indexed death records, and I finally this Debreczeni Eszter record that gives a quick snapshot of her life!

She died 1913 Oct 31 at 2:00. Her name Finta Andrásné (Mrs. András Finta), Debreczeni Eszter. She was 58 years old (born about 1855) when she died. Her husband was Finta András and her parents were the late Debreczeni Sándor and the late N. Nagy Eszter.

I was still puzzled. Searching for Debreczeni Eszter in 1855 through FamilySearch brought up only the Eszter that was a daughter of János and another Eszter, the daughter of Imre. The table of Túrkeve Reformed Church 1855 christenings was 52 pages long and had 324 entries. Perhaps her entry had been indexed incorrectly. I searched again using only first names and found a possible candidate, Nagy Eszter, who was baptized on March 1. I looked at the 1855 baptismal record again. And then I saw it. The minister didn’t get it wrong, the bride didn’t lie about her age: I needed to read the table better! It turns out two baby girls named Debreczeni Eszter were born on February 23rd, but I hadn’t looked past the first one listed. Look at the last entry in the table below. It is the christening record I was looking for!

Eszter, entry number 33, was born on 23 February and baptized on 1 March. Her parents were listed as Debr. Nagy Sándor and Nosza Nagy Eszter. (Having more than one surname was common in Hungary.) When this baptism was indexed by FamilySearch, the parents were understandably indexed as Nagy Sándor and Nagy Eszter, which also let them hide from me easier.

How did you do with this puzzle? You may have been faster than I was, but I knew something was wrong with my findings, and I stuck with it until I figured it out. Those are also important mathematical skills!

### Factors of 1676:

Since this is my 1676th post, I’ll write a little about the number 1676.

1676 happens to be 200 years before the marriage I wrote about above.

- 1676 is a composite number.
- Prime factorization: 1676 = 2 × 2 × 419, which can be written 1676 = 2² × 419.
- 1676 has at least one exponent greater than 1 in its prime factorization so √1676 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1676 = (√4)(√419) = 2√419.
- The exponents in the prime factorization are 2 and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1) = 3 × 2 = 6. Therefore 1676 has exactly 6 factors.
- The factors of 1676 are outlined with their factor pair partners in the graphic below.

### More About the Number 1676:

From OEIS.org, we learn that **1676** = **1¹ **+ **6² **** **+ **7³** + **6****⁴**^{ }.

1676 is the difference of two squares:

420² – 418² = 1676.

The sum of the even leg and hypotenuse for all ppts (primitive Pythagorean triples) is the square of an odd number. This is a rule for ppts that has been sadly overlooked. Because of this, you can find several ppts that have the sum of the even leg and hypotenuse with the same numerical value. Example (35,12,37), (21,20,29), (7,24,25). If their sum is the square of an odd number, p, the number of ppts is (p-1)/2 ppts. If the sum of the square of an odd number is not prime, then (p-1)/2 Pythagorean triples are produced.

Some are ppts and the others are scalar multiples. Example 15 will produce 4 ppt and 3 scalar multiples.

Since for ppts, the sum of the even leg and the hypotenuse is an odd number squared, and an odd number is the sum of an even and an odd number. (m+n)squared gives the m, n parts for the hypotenuse and even leg of ppts.