TASK DEFINITION: Given a sentence in Tagalog language, translate the sentence to English language keeping the meaning of the original sentence intact.
PROBLEM: Tagalog sentence: Kanyang interes karapat-dapat mas malapit sa Kummer, at humiga / magsinungaling lectured sa kanyang sariling mga resulta sa Kummer 's pantas-aral at ay able sa tama ng ilang mga error na Kummer ay ginawa sa kanyang trabaho sa linya congruences ng degree 3.

SOLUTION: His interests fitted more closely with Kummer, and Lie lectured on his own results in Kummer 's seminar and was able to correct some errors that Kummer had made in his work on line congruences of degree 3.

PROBLEM: Tagalog sentence: Sa kanyang sanaysay Heilbronn din inilapat ang kanyang mga resulta sa primes sa isang arithmetic paglala at sa estima ng sum ng Möbius function.

SOLUTION: In his thesis Heilbronn also applied his result to primes in an arithmetic progression and to estimates of the sum of the Möbius function.

PROBLEM: Tagalog sentence: Luzin ng paaralan ay sa kanyang rurok sa panahon ng taon 1922 sa 1926, ngunit pagkatapos ay Luzin puro sa pagsulat ng kanyang ikalawang monograp sa teorya ng pag-andar at ginugol ng mas kaunting oras sa mga kabataan mathematicians sa paaralan.

SOLUTION:
Luzin's school was at its peak during the years 1922 to 1926, but then Luzin concentrated on writing his second monograph on the theory of functions and spent less time with the young mathematicians in the school.