astronomy

Wilhelm Ljunggren

Wilhelm Ljunggren is a astronomy topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Wilhelm Ljunggren rather than just read about it. In short: Wilhelm Ljunggren (7 October 1905 – 25 January 1973) was a Norwegian mathematician, specializing in number theory. Career Ljunggren was born in Kristiania and finished his secondary education in 1925.

Key takeaways

Wilhelm Ljunggren belongs to astronomy; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Wilhelm Ljunggren to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Wilhelm Ljunggren from memory before moving on to harder problems.

Reference excerpt

Wilhelm Ljunggren (7 October 1905 – 25 January 1973) was a Norwegian mathematician, specializing in number theory.

Career Ljunggren was born in Kristiania and finished his secondary education in 1925. He studied at the University of Oslo, earning a master's degree in 1931 under the supervision of Thoralf Skolem, and found employment as a secondary school mathematics teacher in Bergen, following Skolem who had moved in 1930 to the Chr. Michelsen Institute there. While in Bergen, Ljunggren continued his studies, earning a dr.philos. from the University of Oslo in 1937. In 1938 he moved to work as a teacher at Hegdehaugen in Oslo. In 1943 he became a fellow of the Norwegian Academy of Science and Letters, and he also joined the Selskapet til Vitenskapenes Fremme. He was appointed as a docent at the University of Oslo in 1948, but in 1949 he returned to Bergen as a professor at the recently founded University of Bergen. He moved back to the University of Oslo again in 1956, where he served until his death in 1973 in Oslo.

Research Ljunggren's research concerned number theory, and in particular Diophantine equations. He showed that Ljunggren's equation,

X2 = 2Y4 − 1. has only the two integer solutions (1,1) and (239,13); however, his proof was complicated, and after Louis J. Mordell conjectured that it could be simplified, simpler proofs were published by several other authors. Ljunggren also posed the question of finding the integer solutions to the Ramanujan–Nagell equation

2n − 7 = x2 (or equivalently, of finding triangular Mersenne numbers) in 1943, independently of Srinivasa Ramanujan who had asked the same question in 1913. Ljunggren's publications are collected in a book edited by Paulo Ribenboim.

References

Illustrations

Wilhelm Ljunggren: Wilhelm Ljunggren — Wilhelm Ljunggren

Worked examples

Example 1 — a first encounter with Wilhelm Ljunggren

Start with the simplest possible case. Write down what Wilhelm Ljunggren claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Wilhelm Ljunggren before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Wilhelm Ljunggren ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Wilhelm Ljunggren

In research: Wilhelm Ljunggren appears in astronomy research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Wilhelm Ljunggren in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Wilhelm Ljunggren is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1905 births, 1973 deaths, 20th-century Norwegian educators, so understanding it makes those chapters shorter.
In everyday life: Look for Wilhelm Ljunggren outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Wilhelm Ljunggren in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Wilhelm Ljunggren means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Wilhelm Ljunggren out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Wilhelm Ljunggren in simple terms?

Wilhelm Ljunggren (7 October 1905 – 25 January 1973) was a Norwegian mathematician, specializing in number theory. Career Ljunggren was born in Kristiania and finished his secondary education in 1925.

Why does Wilhelm Ljunggren matter?

Because it connects several astronomy ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Wilhelm Ljunggren?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Wilhelm Ljunggren.