22:
209:
343:
293:
390:
263:
239:
138:
497:
51:
481:
90:
401:
561:
556:
537:
73:
423:
113:
34:
44:
38:
30:
298:
55:
428:
268:
505:
491:
453:
371:
244:
220:
533:
477:
117:
445:
437:
124:
517:
513:
449:
406:
365:
426:[On the approximate representation of irrational numbers by rational fractions].
550:
457:
419:
105:
97:
204:{\displaystyle \left|\xi -{\frac {m}{n}}\right|<{\frac {1}{{\sqrt {5}}\,n^{2}}}.}
469:
346:
465:
109:
424:"Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche"
525:
86:
Theorem in number theory that gives a bound on a
Diophantine approximation
441:
89:
This article is about a theorem in number theory. For other uses, see
15:
476:(6th ed.). Oxford science publications. p. 209.
468:, Edward M. Wright, Roger Heath-Brown, Joseph Silverman,
217:
is irrational cannot be omitted. Moreover the constant
512:. Addison-Wesley Publishing Co., Inc., Reading, Mass.
374:
301:
271:
247:
223:
141:
384:
337:
287:
257:
233:
203:
364:The theorem is equivalent to the claim that the
43:but its sources remain unclear because it lacks
8:
496:: CS1 maint: multiple names: authors list (
375:
373:
327:
317:
300:
278:
270:
248:
246:
224:
222:
189:
184:
177:
171:
153:
140:
74:Learn how and when to remove this message
474:An introduction to the Theory of Numbers
489:
338:{\displaystyle \xi =(1+{\sqrt {5}})/2}
7:
241:is the best possible; if we replace
116:. The theorem states that for every
361:such that the formula above holds.
14:
402:Dirichlet's approximation theorem
288:{\displaystyle A>{\sqrt {5}}}
20:
368:of every number is larger than
353:many relatively prime integers
324:
308:
1:
385:{\displaystyle {\sqrt {5}}}
258:{\displaystyle {\sqrt {5}}}
234:{\displaystyle {\sqrt {5}}}
578:
530:Diophantine Approximations
123:there are infinitely many
88:
562:Theorems in number theory
557:Diophantine approximation
114:Diophantine approximation
349:) then there exist only
29:This article includes a
532:. Courier Corporation.
510:Topics in number theory
506:LeVeque, William Judson
472:(2008). "Theorem 193".
58:more precise citations.
386:
339:
289:
259:
235:
205:
429:Mathematische Annalen
387:
340:
290:
260:
236:
206:
372:
299:
269:
245:
221:
139:
213:The condition that
442:10.1007/BF01206656
382:
335:
285:
255:
231:
201:
31:list of references
483:978-0-19-921986-5
380:
322:
283:
253:
229:
196:
182:
161:
118:irrational number
102:Hurwitz's theorem
91:Hurwitz's theorem
84:
83:
76:
569:
543:
521:
501:
495:
487:
461:
407:Langrange number
391:
389:
388:
383:
381:
376:
344:
342:
341:
336:
331:
323:
318:
294:
292:
291:
286:
284:
279:
264:
262:
261:
256:
254:
249:
240:
238:
237:
232:
230:
225:
210:
208:
207:
202:
197:
195:
194:
193:
183:
178:
172:
167:
163:
162:
154:
125:relatively prime
79:
72:
68:
65:
59:
54:this article by
45:inline citations
24:
23:
16:
577:
576:
572:
571:
570:
568:
567:
566:
547:
546:
540:
524:
504:
488:
484:
464:
418:
415:
398:
370:
369:
366:Markov constant
297:
296:
267:
266:
243:
242:
219:
218:
185:
176:
146:
142:
137:
136:
94:
87:
80:
69:
63:
60:
49:
35:related reading
25:
21:
12:
11:
5:
575:
573:
565:
564:
559:
549:
548:
545:
544:
539:978-0486462677
538:
522:
502:
482:
462:
436:(2): 279–284.
414:
411:
410:
409:
404:
397:
394:
379:
334:
330:
326:
321:
316:
313:
310:
307:
304:
282:
277:
274:
265:by any number
252:
228:
200:
192:
188:
181:
175:
170:
166:
160:
157:
152:
149:
145:
104:, named after
85:
82:
81:
39:external links
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
574:
563:
560:
558:
555:
554:
552:
541:
535:
531:
527:
523:
519:
515:
511:
507:
503:
499:
493:
485:
479:
475:
471:
467:
463:
459:
455:
451:
447:
443:
439:
435:
432:(in German).
431:
430:
425:
421:
417:
416:
412:
408:
405:
403:
400:
399:
395:
393:
377:
367:
362:
360:
356:
352:
348:
332:
328:
319:
314:
311:
305:
302:
280:
275:
272:
250:
226:
216:
211:
198:
190:
186:
179:
173:
168:
164:
158:
155:
150:
147:
143:
134:
130:
126:
122:
119:
115:
111:
107:
106:Adolf Hurwitz
103:
99:
98:number theory
92:
78:
75:
67:
57:
53:
47:
46:
40:
36:
32:
27:
18:
17:
529:
509:
473:
470:Andrew Wiles
433:
427:
363:
358:
354:
350:
347:golden ratio
214:
212:
132:
128:
120:
101:
95:
70:
64:October 2022
61:
50:Please help
42:
466:G. H. Hardy
420:Hurwitz, A.
295:and we let
56:introducing
551:Categories
526:Ivan Niven
450:23.0222.02
413:References
135:such that
108:, gives a
492:cite book
458:119535189
303:ξ
151:−
148:ξ
127:integers
528:(2013).
508:(1956).
422:(1891).
396:See also
351:finitely
518:0080682
52:improve
536:
516:
480:
456:
448:
454:S2CID
345:(the
112:on a
110:bound
37:, or
534:ISBN
498:link
478:ISBN
276:>
169:<
446:JFM
438:doi
96:In
553::
514:MR
494:}}
490:{{
452:.
444:.
434:39
392:.
357:,
131:,
100:,
41:,
33:,
542:.
520:.
500:)
486:.
460:.
440::
378:5
359:n
355:m
333:2
329:/
325:)
320:5
315:+
312:1
309:(
306:=
281:5
273:A
251:5
227:5
215:ξ
199:.
191:2
187:n
180:5
174:1
165:|
159:n
156:m
144:|
133:n
129:m
121:ξ
93:.
77:)
71:(
66:)
62:(
48:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.